CN115438088B - Target subgraph searching method in directed graph and related equipment - Google Patents
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Abstract
The invention discloses a target subgraph searching method in a directed graph and related equipment. The method comprises the following steps: obtaining an initial vertex set according to the outgoing degree and the incoming degree of all the vertexes in the original directed graph, wherein the outgoing degree of each vertex in the initial vertex set is not smaller than the outgoing degree target difference value corresponding to the original directed graph, and the incoming degree of each vertex in the initial vertex set is not smaller than the incoming degree target difference value corresponding to the original directed graph; deleting at least one vertex or directed edge in the original directed graph according to the number of the vertices in the initial vertex set to obtain a processed directed graph; and obtaining a target sub-graph in the processing directed graph, wherein the target sub-graph is the sub-graph with the largest number of vertexes contained in the sub-graph meeting the target condition in the original directed graph. The invention can efficiently search partial data with strong correlation from sparse data.
Description
Technical Field
The invention relates to the technical field of graph data processing, in particular to a target subgraph searching method in a directed graph and related equipment.
Background
In practical applications, many data are sparse, for example, community data, and in order to improve data analysis efficiency, it is necessary to extract as many partial data with strong correlation as possible from the sparse data for analysis. However, there is no method for efficiently extracting as much partial data as possible, which has strong correlation, from sparse community data.
Accordingly, there is a need for improvement and advancement in the art.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a target subgraph searching method in a directed graph, which aims to solve the problem that a method for efficiently extracting as much partial data with strong correlation as possible from sparse community data is not available in the prior art.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
in a first aspect of the present invention, a method for searching a target subgraph in a directed graph is provided, where the method includes:
acquiring an original directed graph, acquiring the output degrees and the input degrees of all vertexes in the original directed graph, and acquiring an initial vertex set according to the output degrees and the input degrees of all vertexes, wherein the output degrees of all vertexes in the initial vertex set are not smaller than the output degree target difference value corresponding to the original directed graph, and the input degrees of all vertexes in the initial vertex set are not smaller than the input degree target difference value corresponding to the original directed graph;
deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set to obtain a processed directed graph;
obtaining a target sub-graph in the processing directed graph, wherein the target sub-graph is the sub-graph with the largest number of vertexes contained in the sub-graph meeting the target condition in the original directed graph, and the target condition is that the degree of each vertex in the sub-graph is not smaller than the degree target difference value corresponding to the sub-graph and the degree of each vertex is not smaller than the degree target difference value corresponding to the sub-graph;
The corresponding output target difference value of the graph is the difference value between the number of the vertexes of the graph and a preset output threshold value, and the corresponding input target difference value of the graph is the difference value between the number of the vertexes of the graph and the preset input threshold value.
In a second aspect of the present invention, there is provided a target subgraph lookup device in a directed graph, including:
the initial solution generating module is used for acquiring the output degrees and the input degrees of all vertexes in the original directed graph, and acquiring an initial vertex set according to the output degrees and the input degrees of all vertexes, wherein the output degrees of all vertexes in the initial vertex set are not smaller than the output degree target difference value corresponding to the original directed graph, and the input degrees of all vertexes in the initial vertex set are not smaller than the input degree target difference value corresponding to the original directed graph;
the image preprocessing module is used for deleting at least one vertex or directed edge from the original directed image according to the number of the vertices in the initial vertex set to obtain a processed directed image;
the sub-graph acquisition module is used for acquiring a target sub-graph in the processing directed graph, wherein the target sub-graph is the sub-graph with the largest number of vertexes contained in the sub-graph meeting the target condition in the original directed graph, and the target condition is that the degree of emergence of each vertex in the sub-graph is not smaller than the degree target difference value corresponding to the sub-graph and the degree of incidence of each vertex is not smaller than the degree target difference value corresponding to the sub-graph;
The corresponding output target difference value of the graph is the difference value between the number of the vertexes of the graph and a preset output threshold value, and the corresponding input target difference value of the graph is the difference value between the number of the vertexes of the graph and the preset input threshold value.
In a third aspect of the present invention, a terminal is provided, the terminal comprising a processor, a computer readable storage medium communicatively coupled to the processor, the computer readable storage medium adapted to store a plurality of instructions, the processor adapted to invoke the instructions in the computer readable storage medium to perform steps implementing the method for searching for a target subgraph in a directed graph as described in any of the above.
In a fourth aspect of the present invention, there is provided a computer readable storage medium storing one or more programs executable by one or more processors to implement the steps of the target subgraph lookup method in a directed graph as set forth in any one of the above.
Compared with the prior art, the invention provides a target sub-graph searching method and related equipment in the directed graph, in the target sub-graph searching method provided by the invention, the problem of extracting as much partial data with strong correlation from sparse community data is converted into the problem of searching the maximum sub-graph which satisfies that the output degree of each vertex is not smaller than the output degree target difference value corresponding to the sub-graph and the input degree of each vertex is not smaller than the input degree target difference value corresponding to the sub-graph from the directed graph, and the preprocessing method is adopted, so that the efficiency of sub-graph searching is improved, and the effect of efficiently searching as much partial data with strong correlation from sparse community data is realized.
Drawings
FIG. 1 is a flow chart of an embodiment of a target subgraph lookup method in a directed graph provided by the present invention;
FIG. 2 is a schematic diagram of a directed graph;
FIG. 3 is a schematic diagram of an overall algorithm pseudo code in an embodiment of a target subgraph lookup method in a directed graph provided by the present invention;
FIG. 4 is a schematic diagram of an algorithm pseudo code for searching a target subgraph in a directed graph in processing the directed graph in an embodiment of the target subgraph searching method provided by the present invention;
FIG. 5 is a schematic diagram of an embodiment of a target subgraph lookup device in a directed graph according to the present invention;
fig. 6 is a schematic diagram of an embodiment of a terminal provided by the present invention.
Detailed Description
In order to make the objects, technical solutions and effects of the present invention clearer and more specific, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The target subgraph searching method in the directed graph provided by the invention can be applied to terminals with computing capability, the terminals can execute the target subgraph searching method in the directed graph provided by the invention to acquire target subgraphs, and the terminals can be but are not limited to various computers, mobile terminals, intelligent household appliances, wearable devices and the like.
Example 1
As shown in fig. 1, in one embodiment of the target subgraph lookup method in the directed graph, the method includes the steps of:
s100, acquiring an original directed graph, acquiring the output degrees and the input degrees of all vertexes in the original directed graph, and acquiring an initial vertex set according to the output degrees and the input degrees of all vertexes, wherein the output degrees of all vertexes in the initial vertex set are not smaller than the output degree target difference value corresponding to the original directed graph, and the input degrees of all vertexes in the initial vertex set are not smaller than the input degree target difference value corresponding to the original directed graph.
The original directed graph may be a directed graph generated according to original sparse data to be analyzed, each vertex in the original directed graph may be a data point in the original sparse data, each directed edge in the original directed graph may be a relationship between two data points in the original sparse data, for example, for a directed graph corresponding to community data, a vertex in the directed graph may be each user in a community, a directed edge in the directed graph may be a social media concern relationship between users of the community, etc., and for a directed graph corresponding to biological protein molecular data, a vertex in the directed graph may be an atom, a directed edge in the directed graph may be a chemical bond between molecules, etc.
A simple directed graph may be shown in fig. 2, and in particular, a directed graph G may be represented by g= (V, E), where V represents the set of vertices in the directed graph G and E represents the set of edges in the directed graph G.
In this embodiment, the problem of extracting as many interrelations as possible from the original sparse data is converted into the problem of searching for a target subgraph from the original directed graph, where the target subgraph meets a target condition, and the target condition is: the output degree of each vertex in the subgraph is not smaller than the output degree target difference value corresponding to the subgraph, and the input degree of each vertex is not smaller than the input degree target difference value corresponding to the subgraph.
The corresponding output target difference value of the graph is the difference value of the vertex number of the graph and a preset output threshold value, and the corresponding input target difference value of the graph is the difference value of the vertex number of the graph and the preset input threshold value. The degree of departure and the degree of entry of each vertex in the subgraph are larger than a preset difference value, which indicates that the relevance between the vertices of the subgraph is strong. For convenience of representation, the target subgraph is referred to as a maximum (k, l) -plex, where k is the preset out-degree threshold value, and l is the preset in-degree threshold value, that is, in a directed graph with n vertices, if any vertex in the graph satisfies out-degree greater than or equal to n-k and in-degree greater than or equal to n-l, the directed graph is referred to as a directed (k, l) -plex. As in the original directed graph of fig. 2, the derived subgraph 0,1,2 is a (1, 1) -plex.
In the method provided in this embodiment, as shown in fig. 3, in order to find the target subgraph in the original directed graph, first, a lower bound solution is obtained, and then, graph data preprocessing is performed by using the lower bound solution, and then, accurate searching is performed.
Specifically, the process of obtaining the initial vertex set according to the degree of departure and degree of ingress of the vertices may be:
arranging all the vertexes in the original directed graph from small to large in degree to obtain a first set, and arranging all the vertexes in the original directed graph from small to large in degree to obtain a second set;
sequentially deleting the vertexes in the first set until the vertex with the minimum degree of emergence in the first set is not less than the degree of emergence target difference value corresponding to the original directed graph, and sequentially deleting the vertexes in the second set until the vertex with the minimum degree of incidence in the second set is not less than the degree of incidence target difference value corresponding to the original directed graph;
and a union set is obtained for the first set and the second set, and the initial vertex set is obtained.
After the initial vertex set is obtained, the initial vertex set is utilized to preprocess the original directed graph, namely the original directed graph is reduced, and the efficiency of subsequent accurate searching is improved. Namely, the method provided in this embodiment further includes the steps of:
And S200, deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set, and obtaining a processed directed graph.
The deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set includes:
obtaining a target value, wherein the target value is the maximum value of a first value and vertex values in the initial vertex set, and the first value is the minimum value of a preset out-degree threshold value and a preset in-degree threshold value;
deleting at least one vertex in the original directed graph in a first manner based on the target value; and/or
And deleting at least one directed edge in the original directed graph in a second mode.
In the method provided in this embodiment, two ways of preprocessing the original directed graph may be adopted to implement reduction of the original directed graph, where the two ways may be implemented separately or together.
The deleting at least one vertex in the original directed graph in a first manner includes:
and for one target vertex in the original directed graph, deleting the target vertex in the original directed graph if the degree of departure of the target vertex is smaller than the difference value between the target value and the preset degree threshold value or the degree of arrival of the target vertex is smaller than the difference value between the target value and the preset degree threshold value.
The first mode is a weak reduction mode, and lb=max (|s) is set 0 I, min (k, l)), the weak reduction method is based on the theory that: given a directed graph g= (V, E) and a vertex V E V, if V has an outbound degree less than lb-k or inbound degree less than lb-l, then vertex V cannot appear in a directed (k, l) -plex of size greater than lb, and therefore vertex V can be deleted from the original directed graph without affecting the final target sub-graph lookup result.
The deleting at least one directed edge in the original directed graph in a second manner includes:
for each vertex in the original directed graph, respectively acquiring a corresponding target out-degree set and a target in-degree set, wherein a directed edge from a target vertex to each vertex in the target out-degree set corresponding to the target vertex exists in the original directed graph, and a directed edge from each vertex in the target in-degree set corresponding to the target vertex exists in the original directed graph;
acquiring an outbound degree intersection and an inbound degree intersection between a first target vertex and a second target vertex in the first original directed graph, wherein the outbound degree intersection is an intersection of the target outbound degree sets respectively corresponding to the first target vertex and the second target vertex, and the inbound degree intersection is an intersection of the target inbound degree sets respectively corresponding to the first target vertex and the second target vertex;
And deleting at least one directed edge in the original directed graph according to the number of vertexes in the out-degree intersection and the in-degree intersection.
Said deleting at least one directed edge in said original directed graph based on the number of vertices in said outbound and inbound intersections, comprising:
if the original directed graph has directed edges from the first target vertex to the second target vertex and directed edges from the second target vertex to the first target vertex, and the number of vertices in the out-degree intersection is not greater than a first difference value or the number of vertices in the in-degree intersection is not greater than a second difference value, deleting a connecting edge between the first target vertex and the second target vertex in the original directed graph;
wherein the first difference is a difference of twice the target value and the preset threshold value, and the second difference is a difference of twice the target value and the preset threshold value;
if the connecting edge between the first target vertex and the second target vertex of the original directed graph is a unidirectional connecting edge, and the number of vertices in the degree intersection is not greater than a third difference value or the number of vertices in the degree intersection is not greater than a fourth difference value, deleting the connecting edge between the first target vertex and the second target vertex in the original directed graph;
The third difference value is the first difference value plus 1, and the fourth difference value is the second difference value plus 1.
The second mode is a strong reduction mode, and lb=min (|s) is set 0 I, min (k, l)), the strong reduction method is based on the theory that:
and (3) making:
given a directed graph g= (V, E) and two vertices u, V E V, if:
1. directed edge<u，v>∈E and directed edge<v，u>E and2k orThen u, v cannot occur simultaneously in a directional (k, l) -plex of size greater than lb.
2. Directed edge<u，v>E and directed edgeOr-> And->Or->Then u, v cannot occur simultaneously in a directional (k, l) -plex of size greater than lb.
After the step S200, part of vertices and edges of the original directed graph are deleted, so as to obtain the processed directed graph, and the target subgraph is searched in the processed directed graph, that is, the method further includes the steps of:
s300, acquiring a target subgraph from the processed directed graph, wherein the target subgraph is the subgraph with the largest number of vertexes contained in the subgraph meeting the target condition in the original directed graph, and the target condition is that the degree of departure of each vertex in the subgraph is not smaller than the degree of departure target difference value corresponding to the original directed graph and the degree of arrival of each vertex is not smaller than the degree of arrival target difference value corresponding to the original directed graph.
In one possible implementation, the target subgraph may be solved using a classical integer linear programming method, where the following constraint functions are constructed:
wherein x is v E {0,1}, when x v When=1, it means that vertex v appears in the solution, otherwise it means that vertex v does not appear, e uv E {0,1}, when e uv When=1, it means<u，v>E, otherwise representM is a sufficiently large integer, and m=n may be taken when in use.
In the method provided in this embodiment, as shown in fig. 4, the target subgraph is searched in the processing directed graph based on the idea of the branch-and-bound method. The method specifically comprises the following steps:
adding all vertexes in the processing directed graph into a candidate set, and setting an expansion solution set as an empty set;
selecting a vertex from each branch graph as a root node, generating at least one branch according to a set where the root node is located, and updating the expansion solution set, wherein each branch comprises a branch graph;
when the output degrees of all nodes in the target branch graph are not smaller than the output degree target difference value corresponding to the original directed graph and the input degrees of all nodes are not smaller than the input degree target difference value corresponding to the original directed graph, no vertex is selected as a root node in the target branch graph, otherwise, one vertex is selected as the root node in the target branch graph;
Selecting the graph with the maximum number of vertexes from all the target branch graphs as the target subgraph;
wherein the initial branching diagram is the processing directed diagram.
The generating at least one branch according to the set of the root node and updating the expansion solution set comprises the following steps:
when the root node is in the expansion solution set, a first degree set, a second degree set, a first degree set and a second degree set corresponding to the root node are obtained, wherein the vertexes in the first degree set all belong to the expansion solution set, no directional edge from the root node to each vertex in the second degree set corresponding to the root node exists in a subgraph corresponding to the expansion solution set, the vertexes in the second degree set all belong to the candidate set, no directional edge from the root node to each vertex in the second degree set corresponding to the root node exists in a subgraph corresponding to the candidate set, the vertexes in the first degree set all belong to the expansion solution set, and no directional edge from each vertex in the second degree set corresponding to the root node exists in the subgraph corresponding to the expansion solution set, and the vertexes in the second degree set all belong to the candidate set, and all the vertexes in the subgraph corresponding to the candidate set do not exist;
If the degree of departure of the root node is smaller than a degree of departure target difference value corresponding to the original directed graph, acquiring a first parameter corresponding to the root node, wherein the first parameter is a difference value between a preset degree of departure threshold and the number of vertexes in the first degree set;
generating q from the first parameter and the second set of degree of outtake out +1 degree branches and dividing the first q in the second degree set out Adding vertices to the expansion solution set, where q out For the first parameter, the first q out The branch graphs of the outbound branches are respectively deleted from the branch graph where the root node is located by the first q in the second outbound set out Generated by the vertex, q out The branch graph of +1 out degree branches is obtained by deleting the first q in the second out degree set from the branch graph where the root node is located out Vertices other than the plurality of vertices;
if the ingress of the root node is smaller than the ingress target difference value corresponding to the original directed graph, acquiring a second parameter corresponding to the root node, wherein the second parameter is a difference value between a preset ingress threshold value and the number of vertexes in the first ingress set;
generating q from the first parameter and the second set of incorrectness in +1 degree branches and dividing the first q in the second degree set in Adding vertices to the expansion solution set, where q in For the second parameter, the first q in The branch graphs of the degree-entering branches are respectively deleted from the branch graph where the root node is located by the first q in the second degree-entering set in Generated by the vertex, q in The branch graph of +1 degree branches is obtained by deleting the first q in the second degree set from the branch graph where the root node is located in Vertices other than the plurality of vertices;
and when the root node is in the candidate set, generating two third branches, and adding the root node into the expansion solution set, wherein one third branch is a branch diagram in which the root node is positioned, deleting the root node from the branch diagram in which the root node is positioned, and the other third branch is a branch diagram in which the root node is positioned.
Specifically, if a vertex in the graph satisfies that the degree of occurrence is n-k or greater, the vertex is referred to as k-rational, otherwise, k-joint. Similarly, if a vertex is not less than n-l, then the vertex is said to be l-sampled, otherwise it is said to be l-unsatisfied. In each branch recursion, the algorithm will find the vertex with the smallest degree of emergence and the vertex with the smallest degree of invasiveness for the current instance, assuming that at least one vertex is assumed to be unsatisfied (otherwise the algorithm will not have generated a new branch on this branch because it has found (k, l) -plex). There are two branching methods by determining whether the vertex is in the expansion solution set F or in the candidate set U.
Assume that
In the following description of the branching methods in the two sets, the description of the values is that G hereinafter refers to the branching diagram that needs to generate the next generation branching diagram, i.e., the branching diagram G is generated by the branching rules hereinafter.
Branching rule one: branching in F
Let the vertex w be the k-unsatisfied vertex in the F set (i-unsatisfied same applies), let
Since vertex w is k-unsatisfied, q out ＜p out . And (3) the following steps: wherein->Is arbitrary.
The branching rule one will generate q out +1 branches:
branch 1: vertex x is eliminated from graph G 1
Branch 2: let f=f { x } u } 1 And remove vertex x from the graph 2
Branch 3: let f=f { x } u } 1 ，x 2 And remove vertex x from the graph 3
…
Branch q out : order theAnd the vertex is omitted from the figure>
Branch q out +1: order theAnd the vertex is omitted from the figure>
Branching rule two: branching in U
Assuming vertex w is the k-unsatisfied vertex in the F set (i-unsatisfied theorem), then branch rule two will result in 2 branches:
branch 1: vertex w is omitted from graph G
Branch 2: let f=f { w }.
For each newly generated branch graph, if any node cannot be added to the expansion solution in the branch graph, the branch graph is not branched any more, and the branch graph is called a target branch graph. And each time a new target branch diagram is generated, comparing the new target branch diagram with the stored target branch diagram, and selecting one reservation with larger node number and deleting the other reservation.
In the branching process, if the number of nodes in the branch graph is smaller than the current existing target branch graph, even if the unsatisfied vertex still exists in the branch graph, the node can be not branched.
And acquiring the final target branch graph as the target subgraph, and after the target subgraph is obtained, extracting corresponding data from the original sparse data according to the target subgraph as data to be analyzed for analysis.
In summary, the present embodiment provides a method for searching a target subgraph in a directed graph, which converts the problem of extracting as much of partial data with strong correlation as possible from sparse data into the problem of searching the maximum subgraph from the directed graph, wherein the degree of departure of each vertex is not less than the degree target difference value corresponding to the original directed graph and the degree of entrance of each vertex is not less than the degree target difference value corresponding to the original directed graph.
It should be understood that, although the steps in the flowcharts shown in the drawings of the present specification are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least a portion of the steps in the flowcharts may include a plurality of sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, the order in which the sub-steps or stages are performed is not necessarily sequential, and may be performed in turn or alternately with at least a portion of the sub-steps or stages of other steps or other steps.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
Example two
Based on the above embodiment, the present invention further provides a target subgraph lookup device in a directed graph, as shown in fig. 5, where the target subgraph lookup device in the directed graph includes:
the initial solution generating module is configured to obtain an original directed graph, obtain the output degrees and the input degrees of all vertices in the original directed graph, and obtain an initial vertex set according to the output degrees and the input degrees of all vertices, where the output degrees of each vertex in the initial vertex set are not less than an output target difference value corresponding to the original directed graph, and the input degrees of each vertex in the initial vertex set are not less than an input target difference value corresponding to the original directed graph, as described in embodiment one;
the graph preprocessing module is configured to delete at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set, so as to obtain a processed directed graph, which is described in embodiment one;
the sub-graph obtaining module is configured to obtain a target sub-graph from the processed directed graph, where the target sub-graph is a sub-graph with the largest number of vertices included in the sub-graph that satisfies a target condition in the original directed graph, and the target condition is that the degree of egress of each vertex in the sub-graph is not less than a degree of egress target difference value corresponding to the original directed graph and the degree of ingress of each vertex is not less than a degree of egress target difference value corresponding to the original directed graph, as described in embodiment one.
Example III
Based on the above embodiment, the present invention also correspondingly provides a terminal, as shown in fig. 6, which includes a processor 10 and a memory 20. Fig. 6 shows only some of the components of the terminal, but it should be understood that not all of the illustrated components are required to be implemented and that more or fewer components may alternatively be implemented.
The memory 20 may in some embodiments be an internal storage unit of the terminal, such as a hard disk or a memory of the terminal. The memory 20 may in other embodiments also be an external storage device of the terminal, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card) or the like, which are provided on the terminal. Further, the memory 20 may also include both an internal storage unit and an external storage device of the terminal. The memory 20 is used for storing application software and various data installed in the terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, the memory 20 stores a directed graph target sub-graph lookup program 30, and the directed graph target sub-graph lookup program 30 is executable by the processor 10 to implement the directed graph target sub-graph lookup method of the present application.
The processor 10 may in some embodiments be a central processing unit (Central Processing Unit, CPU), microprocessor or other chip for executing program code or processing data stored in the memory 20, such as performing the target subgraph lookup method in the directed graph, etc.
In one embodiment, the following steps are implemented when the processor 10 executes the target subgraph lookup program 30 in the directed graph in the memory 20:
acquiring an original directed graph, acquiring the output degrees and the input degrees of all vertexes in the original directed graph, and acquiring an initial vertex set according to the output degrees and the input degrees of all vertexes, wherein the output degrees of all vertexes in the initial vertex set are not smaller than the output degree target difference value corresponding to the original directed graph, and the input degrees of all vertexes in the initial vertex set are not smaller than the input degree target difference value corresponding to the original directed graph;
deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set to obtain a processed directed graph;
and obtaining a target subgraph from the processed directed graph, wherein the target subgraph is the subgraph with the largest number of vertexes contained in the subgraph meeting the target condition in the original directed graph, and the target condition is that the degree of departure of each vertex in the subgraph is not smaller than the degree target difference value corresponding to the original directed graph and the degree of arrival of each vertex is not smaller than the degree target difference value corresponding to the original directed graph.
The deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set includes:
obtaining a target value, wherein the target value is the minimum value of a first value and the vertex values in the initial vertex set, the first value is the minimum value of a preset degree threshold and a preset degree threshold, the preset degree threshold is the difference value between the number of all the vertices in the original directed graph and the degree target difference value corresponding to the original directed graph, and the preset degree threshold is the difference value between the number of all the vertices in the original directed graph and the degree target difference value corresponding to the original directed graph;
deleting at least one vertex in the original directed graph in a first manner based on the target value; and/or
And deleting at least one directed edge in the original directed graph in a second mode.
The deleting at least one vertex in the original directed graph in a first manner includes:
and for one target vertex in the original directed graph, deleting the target vertex in the original directed graph if the degree of departure of the target vertex is smaller than the difference value between the target value and the preset degree threshold value or the degree of arrival of the target vertex is smaller than the difference value between the target value and the preset degree threshold value.
The deleting at least one directed edge in the original directed graph in a second manner includes:
for each vertex in the original directed graph, respectively acquiring a corresponding target out-degree set and a target in-degree set, wherein a directed edge from a target vertex to each vertex in the target out-degree set corresponding to the target vertex exists in the original directed graph, and a directed edge from each vertex in the target in-degree set corresponding to the target vertex exists in the original directed graph;
acquiring an outbound degree intersection and an inbound degree intersection between a first target vertex and a second target vertex in the first original directed graph, wherein the outbound degree intersection is an intersection of the target outbound degree sets respectively corresponding to the first target vertex and the second target vertex, and the inbound degree intersection is an intersection of the target inbound degree sets respectively corresponding to the first target vertex and the second target vertex;
and deleting at least one directed edge in the original directed graph according to the number of vertexes in the out-degree intersection and the in-degree intersection.
Said deleting at least one directed edge in said original directed graph based on the number of vertices in said outbound and inbound intersections, comprising:
If the original directed graph has directed edges from the first target vertex to the second target vertex and directed edges from the second target vertex to the first target vertex, and the number of vertices in the out-degree intersection is not greater than a first difference value or the number of vertices in the in-degree intersection is not greater than a second difference value, deleting a connecting edge between the first target vertex and the second target vertex in the original directed graph;
wherein the first difference is a difference of twice the target value and the preset threshold value, and the second difference is a difference of twice the target value and the preset threshold value;
if the connecting edge between the first target vertex and the second target vertex of the original directed graph is a unidirectional connecting edge, and the number of vertices in the degree intersection is not greater than a third difference value or the number of vertices in the degree intersection is not greater than a fourth difference value, deleting the connecting edge between the first target vertex and the second target vertex in the original directed graph;
the third difference value is the first difference value plus 1, and the fourth difference value is the second difference value plus 1.
The obtaining the target subgraph in the processing directed graph comprises the following steps:
adding all vertexes in the processing directed graph into a candidate set, and setting an expansion solution set as an empty set;
selecting a vertex from each branch graph as a root node, generating at least one branch according to a set where the root node is located, and updating the expansion solution set, wherein each branch comprises a branch graph;
when the output degrees of all nodes in a target branch graph are not smaller than the output degree target difference value corresponding to the target branch graph and the input degrees of all nodes are not smaller than the input degree target difference value corresponding to the target branch graph, no vertex is selected from the target branch graph as a root node;
selecting the graph with the maximum number of vertexes from all the target branch graphs as the target subgraph;
wherein the initial branching diagram is the processing directed diagram.
The generating at least one branch according to the set of the root node and updating the expansion solution set comprises the following steps:
when the root node is in the expansion solution set, a first degree set, a second degree set, a first degree set and a second degree set corresponding to the root node are obtained, wherein the vertexes in the first degree set all belong to the expansion solution set, no directional edge from the root node to the root node in the first degree set corresponding to the root node exists in a subgraph corresponding to the expansion solution set, the vertexes in the second degree set all belong to the candidate set, no directional edge from the root node to each vertex in the second degree set corresponding to the root node exists in a subgraph corresponding to the candidate set, the vertexes in the first degree set all belong to the expansion solution set, and no directional edge from each vertex to the root node in the first degree set corresponding to the root node exists in the subgraph corresponding to the expansion solution set, and the vertexes in the second degree set all belong to the candidate set, and no directional edge from the vertex to the root node in the candidate set exists in the subgraph;
If the degree of emergence of the root node is smaller than a degree of emergence target difference value corresponding to a branch diagram where the root node is located, acquiring a first parameter corresponding to the root node, wherein the first parameter is a difference value between a preset degree of emergence threshold and the number of vertexes in the first degree of emergence set;
according to the first parameter and the second outputAggregation generation q out +1 degree branches and dividing the first q in the second degree set out Adding vertices to the expansion solution set, where q out For the first parameter, the first q out The branch graphs of the outbound branches are respectively deleted from the branch graph where the root node is located by the first q in the second outbound set out Generated by the vertex, q out The branch graph of +1 out degree branches is obtained by deleting the first q in the second out degree set from the branch graph where the root node is located out Vertices other than the plurality of vertices;
if the ingress of the root node is smaller than the ingress target difference value corresponding to the branch graph where the root node is located, acquiring a second parameter corresponding to the root node, wherein the second parameter is a difference value between a preset ingress threshold value and the number of vertexes in the first ingress set;
generating q from the first parameter and the second set of incorrectness in +1 degree branches and dividing the first q in the second degree set in Adding vertices to the expansion solution set, where q in For the second parameter, the first q in The branch graphs of the degree-entering branches are respectively deleted from the branch graph where the root node is located by the first q in the second degree-entering set in Generated by the vertex, q in The branch graph of +1 degree branches is obtained by deleting the first q in the second degree set from the branch graph where the root node is located in Vertices other than the plurality of vertices;
and when the root node is in the candidate set, generating two third branches, and adding the root node into the expansion solution set, wherein one third branch is a branch diagram in which the root node is positioned, deleting the root node from the branch diagram in which the root node is positioned, and the other third branch is a branch diagram in which the root node is positioned.
Example IV
The present invention also provides a computer readable storage medium having stored therein one or more programs executable by one or more processors to implement the steps of the target subgraph lookup method in a directed graph as described above.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. A method for searching a target subgraph in a directed graph, the method comprising:
obtaining an original directed graph, obtaining the output degrees and the input degrees of all vertexes in the original directed graph, obtaining an initial vertex set according to the output degrees and the input degrees of all vertexes, wherein the output degrees of all vertexes in the initial vertex set are not smaller than an output degree target difference value corresponding to the original directed graph, the input degrees of all vertexes in the initial vertex set are not smaller than an input degree target difference value corresponding to the original directed graph, the original directed graph is obtained based on community data, the vertexes in the original directed graph represent each user in a community, and edges in the original directed graph represent social media attention relations among users of the community;
deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set to obtain a processed directed graph;
obtaining a target sub-graph in the processing directed graph, wherein the target sub-graph is the sub-graph with the largest number of vertexes contained in the sub-graph meeting the target condition in the original directed graph, and the target condition is that the degree of each vertex in the sub-graph is not smaller than the degree target difference value corresponding to the sub-graph and the degree of each vertex is not smaller than the degree target difference value corresponding to the sub-graph;
Extracting corresponding data from the community data based on the target subgraph as data to be analyzed for analysis;
the corresponding degree target difference value of the graph is the difference value of the vertex number of the graph and a preset degree threshold value, and the corresponding degree target difference value of the graph is the difference value of the vertex number of the graph and the preset degree threshold value;
the obtaining the target subgraph in the processing directed graph comprises the following steps:
adding all vertexes in the processing directed graph into a candidate set, and setting an expansion solution set as an empty set;
selecting a vertex from each branch graph as a root node, generating at least one branch according to a set where the root node is located, and updating the expansion solution set, wherein each branch comprises a branch graph;
when the output degrees of all nodes in a target branch graph are not smaller than the output degree target difference value corresponding to the target branch graph and the input degrees of all nodes are not smaller than the input degree target difference value corresponding to the target branch graph, no vertex is selected from the target branch graph as a root node;
selecting the graph with the maximum number of vertexes from all the target branch graphs as the target subgraph;
wherein the initial branch graph is the processing directed graph;
The generating at least one branch according to the set of the root node and updating the expansion solution set comprises the following steps:
when the root node is in the expansion solution set, a first degree set, a second degree set, a first degree set and a second degree set corresponding to the root node are obtained, wherein the vertexes in the first degree set all belong to the expansion solution set, no directional edge from the root node to the root node in the first degree set corresponding to the root node exists in a subgraph corresponding to the expansion solution set, the vertexes in the second degree set all belong to the candidate set, no directional edge from the root node to each vertex in the second degree set corresponding to the root node exists in a subgraph corresponding to the candidate set, the vertexes in the first degree set all belong to the expansion solution set, and no directional edge from each vertex to the root node in the first degree set corresponding to the root node exists in the subgraph corresponding to the expansion solution set, and the vertexes in the second degree set all belong to the candidate set, and no directional edge from the vertex to the root node in the candidate set exists in the subgraph;
If the degree of emergence of the root node is smaller than a degree of emergence target difference value corresponding to a branch diagram where the root node is located, acquiring a first parameter corresponding to the root node, wherein the first parameter is a difference value between a preset degree of emergence threshold and the number of vertexes in the first degree of emergence set;
generating q from the first parameter and the second set of degree of outtake out +1 degree branches and dividing the first q in the second degree set out Adding vertices to the expansion solution set, where q out For the first parameter, the first q out The branch graphs of the outbound branches are respectively deleted from the branch graph where the root node is located by the first q in the second outbound set out Generated by the vertex, q out The branch graph of +1 out degree branches is obtained by deleting the first q in the second out degree set from the branch graph where the root node is located out Vertices other than the plurality of vertices;
if the ingress of the root node is smaller than the ingress target difference value corresponding to the branch graph where the root node is located, acquiring a second parameter corresponding to the root node, wherein the second parameter is a difference value between a preset ingress threshold value and the number of vertexes in the first ingress set;
generating q from the first parameter and the second set of incorrectness in +1 degree branches and dividing the first q in the second degree set in Adding vertices to the expansion solution set, where q in For the second parameter, the first q in The branch graphs of the degree-entering branches are respectively deleted from the branch graph where the root node is located by the first q in the second degree-entering set in Generated by the vertex, q in The branch graph of +1 degree branches is obtained by deleting the first q in the second degree set from the branch graph where the root node is located in Vertices other than the plurality of verticesAnd is generated;
and when the root node is in the candidate set, generating two third branches, and adding the root node into the expansion solution set, wherein one third branch is a branch diagram in which the root node is positioned, deleting the root node from the branch diagram in which the root node is positioned, and the other third branch is a branch diagram in which the root node is positioned.
2. The method for searching for the target subgraph in the directed graph according to claim 1, wherein said deleting at least one vertex or directed edge in the original directed graph according to the number of vertices in the initial vertex set includes:
obtaining a target value, wherein the target value is the maximum value of a first value and vertex values in the initial vertex set, and the first value is the minimum value of the preset out-degree threshold value and the preset in-degree threshold value;
Deleting at least one vertex in the original directed graph in a first manner based on the target value; and/or
And deleting at least one directed edge in the original directed graph in a second mode.
3. The method for searching for the target subgraph in the directed graph according to claim 2, wherein said adopting the first mode to delete at least one vertex in the original directed graph includes:
and for one target vertex in the original directed graph, deleting the target vertex in the original directed graph if the degree of departure of the target vertex is smaller than the difference value between the target value and the preset degree threshold value or the degree of arrival of the target vertex is smaller than the difference value between the target value and the preset degree threshold value.
4. The method for searching the target subgraph in the directed graph according to claim 2, wherein said deleting at least one directed edge in the original directed graph in the second manner includes:
for each vertex in the original directed graph, respectively acquiring a corresponding target out-degree set and a target in-degree set, wherein a directed edge from a target vertex to each vertex in the target out-degree set corresponding to the target vertex exists in the original directed graph, and a directed edge from each vertex in the target in-degree set corresponding to the target vertex exists in the original directed graph;
Acquiring an outbound degree intersection and an inbound degree intersection between a first target vertex and a second target vertex in a first original directed graph, wherein the outbound degree intersection is an intersection of the target outbound degree sets respectively corresponding to the first target vertex and the second target vertex, and the inbound degree intersection is an intersection of the target inbound degree sets respectively corresponding to the first target vertex and the second target vertex;
and deleting at least one directed edge in the original directed graph according to the number of vertexes in the out-degree intersection and the in-degree intersection.
5. A method of searching for a target subgraph in a directed graph according to claim 3 in which said deleting at least one directed edge in said original directed graph based on the number of vertices in said degree intersection and said degree intersection comprises:
if the original directed graph has directed edges from the first target vertex to the second target vertex and directed edges from the second target vertex to the first target vertex, and the number of vertices in the out-degree intersection is not greater than a first difference value or the number of vertices in the in-degree intersection is not greater than a second difference value, deleting a connecting edge between the first target vertex and the second target vertex in the original directed graph;
Wherein the first difference is a difference of twice the target value and the preset threshold value, and the second difference is a difference of twice the target value and the preset threshold value;
if the connecting edge between the first target vertex and the second target vertex of the original directed graph is a unidirectional connecting edge, and the number of vertices in the degree intersection is not greater than a third difference value or the number of vertices in the degree intersection is not greater than a fourth difference value, deleting the connecting edge between the first target vertex and the second target vertex in the original directed graph;
the third difference value is the first difference value plus 1, and the fourth difference value is the second difference value plus 1.
6. A target subgraph lookup device in a directed graph, comprising:
the initial solution generating module is used for acquiring the output degrees and the input degrees of all vertexes in the original directed graph, acquiring an initial vertex set according to the output degrees and the input degrees of all vertexes, wherein the output degrees of all vertexes in the initial vertex set are not smaller than an output target difference value corresponding to the original directed graph, the input degrees of all vertexes in the initial vertex set are not smaller than an input target difference value corresponding to the original directed graph, the original directed graph is obtained based on community data, the vertexes in the original directed graph represent each user in a community, and the edges in the original directed graph represent social media attention relations among users of the community;
The image preprocessing module is used for deleting at least one vertex or directed edge from the original directed image according to the number of the vertices in the initial vertex set to obtain a processed directed image;
the sub-graph acquisition module is used for acquiring a target sub-graph in the processing directed graph, wherein the target sub-graph is the sub-graph with the largest number of vertexes contained in the sub-graph meeting the target condition in the original directed graph, and the target condition is that the degree of emergence of each vertex in the sub-graph is not smaller than the degree target difference value corresponding to the sub-graph and the degree of incidence of each vertex is not smaller than the degree target difference value corresponding to the sub-graph;
extracting corresponding data from the community data based on the target subgraph as data to be analyzed for analysis;
the corresponding degree target difference value of the graph is the difference value of the vertex number of the graph and a preset degree threshold value, and the corresponding degree target difference value of the graph is the difference value of the vertex number of the graph and the preset degree threshold value;
the obtaining the target subgraph in the processing directed graph comprises the following steps:
adding all vertexes in the processing directed graph into a candidate set, and setting an expansion solution set as an empty set;
Selecting a vertex from each branch graph as a root node, generating at least one branch according to a set where the root node is located, and updating the expansion solution set, wherein each branch comprises a branch graph;
when the output degrees of all nodes in a target branch graph are not smaller than the output degree target difference value corresponding to the target branch graph and the input degrees of all nodes are not smaller than the input degree target difference value corresponding to the target branch graph, no vertex is selected from the target branch graph as a root node;
selecting the graph with the maximum number of vertexes from all the target branch graphs as the target subgraph;
wherein the initial branch graph is the processing directed graph;
the generating at least one branch according to the set of the root node and updating the expansion solution set comprises the following steps:
when the root node is in the expansion solution set, a first degree set, a second degree set, a first degree set and a second degree set corresponding to the root node are obtained, wherein the vertexes in the first degree set all belong to the expansion solution set, no directional edge from the root node to the root node in the first degree set corresponding to the root node exists in a subgraph corresponding to the expansion solution set, the vertexes in the second degree set all belong to the candidate set, no directional edge from the root node to each vertex in the second degree set corresponding to the root node exists in a subgraph corresponding to the candidate set, the vertexes in the first degree set all belong to the expansion solution set, and no directional edge from each vertex to the root node in the first degree set corresponding to the root node exists in the subgraph corresponding to the expansion solution set, and the vertexes in the second degree set all belong to the candidate set, and no directional edge from the vertex to the root node in the candidate set exists in the subgraph;
If the degree of emergence of the root node is smaller than a degree of emergence target difference value corresponding to a branch diagram where the root node is located, acquiring a first parameter corresponding to the root node, wherein the first parameter is a difference value between a preset degree of emergence threshold and the number of vertexes in the first degree of emergence set;
generating q from the first parameter and the second set of degree of outtake out +1 degree branches and dividing the first q in the second degree set out Adding vertices to the expansion solution set, where q out For the first parameter, the first q out The branch graphs of the outbound branches are respectively deleted from the branch graph where the root node is located by the first q in the second outbound set out Generated by the vertex, q out The branch graph of +1 out degree branches is obtained by deleting the first q in the second out degree set from the branch graph where the root node is located out Vertices other than the plurality of vertices;
if the ingress of the root node is smaller than the ingress target difference value corresponding to the branch graph where the root node is located, acquiring a second parameter corresponding to the root node, wherein the second parameter is a difference value between a preset ingress threshold value and the number of vertexes in the first ingress set;
generating q from the first parameter and the second set of incorrectness in +1 degree branches and dividing the first q in the second degree set in Adding vertices to the expansion solution set, where q in For the second parameter, the first q in The branch graphs of the degree-entering branches are respectively deleted from the branch graph where the root node is located by the first q in the second degree-entering set in Generated by the vertex, q in The branch graph of +1 degree branches is obtained by deleting the first q in the second degree set from the branch graph where the root node is located in Vertices other than the plurality of vertices;
and when the root node is in the candidate set, generating two third branches, and adding the root node into the expansion solution set, wherein one third branch is a branch diagram in which the root node is positioned, deleting the root node from the branch diagram in which the root node is positioned, and the other third branch is a branch diagram in which the root node is positioned.
7. A terminal, the terminal comprising: a processor, a computer readable storage medium communicatively coupled to the processor, the computer readable storage medium adapted to store a plurality of instructions, the processor adapted to invoke the instructions in the computer readable storage medium to perform the steps of implementing the method for target subgraph lookup in a directed graph as set forth in any of the above claims 1-5.
8. A computer readable storage medium storing one or more programs executable by one or more processors to implement the steps of the target subgraph lookup method in a directed graph as claimed in any one of claims 1-5.
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