CN113626657A - Method for discovering densely connected sub-networks by multi-value attribute graph structure - Google Patents
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Abstract
The invention provides a method for discovering densely connected sub-networks by a multi-value attribute graph structure. The method for discovering the densely connected sub-networks by the multi-value attribute graph structure comprises the following steps: s1, reading a multi-value attribute graph G, limiting I, fixing a node set F, dimension d and influence F. The invention discovers a densely connected sub-network technology and a framework by designing a multi-value attribute graph structure, is mainly used for detecting interested communities of each node in a multi-value network associated with d-value attributes, can find out sub-graphs with close connection, can consider a plurality of attributes while ensuring close connection, and meanwhile, communities identified by the model constructed by the invention cannot be dominated by other communities in a d-dimension attribute space, so that all interesting communities in the d-dimension attribute space can be captured to the maximum extent, thereby realizing the search of various attribute nodes in the multi-value attribute graph and having better application value to a certain extent.
Description
Technical Field
The invention relates to the field of graph databases, in particular to a method for discovering densely connected sub-networks by a multi-value attribute graph structure.
Background
Many real-world networks, such as social networks, are composed of community structures. Discovery of communities from a network is a fundamental problem in network analysis, and in recent years, a query-based community discovery problem called community search has attracted attention due to its large number of applications in database communities. The goal of the community search problem is to find densely connected subgraphs in the network that satisfy the query conditions. Community search is a fundamental problem in network analysis, and has recently received much attention due to its wide application, such as protein structure analysis, campaign organization, advertisement, etc. The community search problem is a query-dependent community discovery problem that requires finding densely connected subgraphs in a network given the query conditions.
However, for a widely existing multi-valued network, where each node has d numerical attributes, most existing algorithms either ignore the attributes of the node completely or only consider one attribute, while most existing community search algorithms either ignore the numerical attributes completely or only consider one numerical attribute of the node and therefore cannot be used directly to answer these questions.
In addition, in many applications, a graph typically involves nodes with multidimensional numerical attributes, and according to some ranking functions, a set of highly connected nodes and an optimal node need to be retrieved, and it is well known that if no ranking function is specified, skyline will return candidates for the optimal object; however, because the communities with high average values in each dimension may also be dominated by other communities to fully describe the interesting communities, the simple method cannot completely capture all interesting communities in the d-dimension attribute space, and therefore, a new community model is provided based on the concepts of k-core and skyline.
Therefore, there is a need to provide a method for discovering densely connected sub-networks by using a multi-valued attribute diagram structure to solve the above technical problems.
Disclosure of Invention
The invention provides a method for discovering densely connected sub-networks by a multi-value attribute graph structure, which solves the problem that all interesting communities in a d-dimensional attribute space cannot be completely captured by the traditional community search problem.
In order to solve the above technical problem, the method for discovering a densely connected sub-network by using a multi-valued attribute graph structure provided by the present invention comprises the following steps:
s1, reading a multi-value attribute graph G, limiting I, fixing a node set F, dimension d and influence F;
s2, deleting invalid nodes in the graph according to the limitation I, calculating a maximum connection k-core subgraph H in the graph, and calculating the maximum value f of the H on the 1 st dimension1；
S3, passing through the maximum value f in the 1 st dimension1Further limiting accurately, calculating the maximum value f of 2 nd dimension2Obtaining a skyline community;
s4, then passing through the limit f1And f2Further calculating other skyline communities;
s5, when d is 3, it is necessary to fix a node u first and find out all f on d-th dimension3The value is found by calling the 2 nd dimension algorithm to each f3Skyline community of 2 dimensions of value, finally f1、f2And f3Merging to obtain 3-dimensional skyline community;
s6, when d is larger than or equal to 3, the main difference is that the skyline community of (d-1) dimension is calculated by recursively calling, when d is 3, the recursive process is terminated, because the 3 rd dimension algorithm is called to calculate the 3 rd dimension skyline community, and finally f is calculated1、f2、f3And (d-1) the skyline community is combined to obtain the demand.
Preferably, when the k-core subgraph H and the maximum value f are calculated in S2, the maximum value f of the 1 st dimension of the graph G is calculated1Is marked as f in all the maximum connection subgraphs k-core1At one maximumThe 1 st dimension in the k-core subgraph H is connected to have one as f1By recursively deleting node values less than f1Nodes until no k-core exists in the graph.
Preferably, the greatly-connected sub-graph k-core H in S2 may not be a skyline community, since H' may have the same f1Value, but f2CommunntyH 'with a value greater than H is dominant, however, such a community H' must be contained in H because of its f1The value is the same as H, which is the largest of all k-cores.
Preferably, in order to find a skyline community in S3, the same procedure as in S2 may be applied to calculate the maximum f2The value is denoted as f2All the sub-k-cores contained in H are derived from H2The result of the representation k-core must be one (f)1(H1)，f2(H1) Skyline community of, wherein f1(H1)＝f1*，f2(H1)＝f2Due to f2Is the largest of all the current k-cores, so no other k-core can dominate it in the 2 nd dimension.
Preferably, the specific step of calculating the other skyline communities in S4 is to refine the previous constraint conditions according to a calculation step similar to S1, where the value of the 2 nd dimension is greater than f2, and the value of the 1 st dimension is greater than f1, because the nodes of the 1 st dimension not greater than f1 and the value of the 2 nd dimension not greater than f2 cannot be included in the undiscovered skyline communities.
Preferably, f in S31All have the same f2The value of k-core is the largest and therefore there is no k-core that dominates it, which must be a skyline community since the previous recursion process ensured that the final k-core was the largest.
Preferably, in S5, for skyline community with 3 dimensions, the algorithm is based on a dimension reduction idea, which includes the following three steps:
s51, first, derive all possible f that skyline community may possess in dimension 33A value;
s52, secondly, for each possible f3Value (in f)3Representation), we find x1And x2All 2D skyline communications in a dimension, let f be3Value equal to f3Herein, skyline communities based on the 1 st and 2 nd dimensions are referred to as 2D skylinecocommunities, while all skyline communities based on three dimensions are referred to as 3D skyline communities;
s53, finally, for all possible f3And combining the generated skyline communities, and calling a traditional skyline algorithm to determine all the 3D skyline communities.
Preferably, F is provided in S533Is all possible f3A simple solution to the set of values, for S51, is to put F3Set as all x in G3Set of node values (x)3Representing the 3 rd dimension of the node) because f of all skyline communities3The value must be acquired from the set of all F3 node values, and S52 may be performed in such a manner that all x' S are deleted3Value less than f3Node of x, fixing node u as xu3＝f3(a fixed node indicates that the node cannot be deleted by the algorithm), it should be noted that there is only one xu of the node u3＝f3Is fixed because, according to the assumptions, all x3The values form a total order using the constraint I ═ x3≥f3The 2D skyline community algorithm is called to calculate x by the fixed point set F ═ u ═ and the fixed point set F ═ u }1And 2D skyline community in the x2 dimension, it can be easily seen that the final community is 2Dskyline community (x1And x2Dimensionally), f3Value equal to f3*。
Preferably, in S6, for skyline communications with dimensions greater than 3, the general process of changing 3-dimensional skyline communications to more dimensions is very similar to that of 3-dimensional, and the main difference is that the algorithm recursively calls itself with the parameter D-1 to calculate (D-1) dimension skyline communications, and when D is 3, the recursive process terminates because the 3-dimensional algorithm is called to calculate 3D skyline communications.
Compared with the related art, the method for discovering the densely connected sub-networks by the multi-value attribute graph structure has the following beneficial effects:
the invention discovers densely connected sub-network technology and framework by designing a multi-value attribute graph structure, is mainly used for detecting interested communities of each node in a multi-value network and associated with d number of value attributes, can find out sub-graphs with close connection, can consider a plurality of attributes while ensuring close connection, meanwhile, the communities identified by the model constructed by the invention cannot be dominated by other communities in the d-dimensional attribute space, further capturing all interesting communities in the d-dimensional attribute space to the maximum extent, wherein the model adopts k-core and skyline, utilizes the characteristics of the real world network, the influence of a plurality of factors can be considered simultaneously, and different from the prior scheme, the algorithm considers the attribute values of a plurality of nodes, the method and the device can search various attribute nodes in the multi-value attribute graph, and have better application value to a certain extent.
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FIG. 1 is a flow chart of a method for discovering densely connected sub-networks by a multi-valued attribute graph structure provided by the present invention;
FIG. 2 is a schematic diagram of the skyline community structure in the method for discovering densely connected sub-networks according to the multi-value property graph structure provided by the present invention.
Detailed Description
The invention is further described with reference to the following figures and embodiments.
Referring to fig. 1 and fig. 2 in combination, fig. 1 is a flow chart of a method for discovering a densely connected sub-network according to the multi-valued attribute diagram structure provided in the present invention; FIG. 2 is a schematic diagram of the skyline community structure in the method for discovering densely connected sub-networks according to the multi-value property graph structure provided by the present invention. A method for discovering densely connected sub-networks by a multi-valued attribute graph structure, comprising the steps of:
s1, reading a multi-value attribute graph G, limiting I, fixing a node set F, dimension d and influence F;
s2, according to the limitation I, deleting invalid nodes in the graph and calculating the graphConnecting the medium and large k-core subgraphs H, and calculating the maximum value f of H in the 1 st dimension1(ii) a By a maximum value f in the 1 st dimension1Further limiting accurately, calculating the maximum value f of 2 nd dimension2Obtaining a skyline community;
wherein, the d-th dimension maximum value f is required to be found, and the 1 st dimension maximum value f of the graph G is calculated1Is marked as f in all the maximum connection subgraphs k-core1The value of 1 st dimension in a maximal connected subgraph k-core subgraph H is f1By recursively deleting node values less than f1Note that nodes until no k-core exists in the graph: may not be a skyline community because H' may have the same f1Value, but f2CommunntyH 'with a value greater than H is dominant, however, such a community H' must be contained in H because of its f1The value is the same as H, which is the largest of all k-cores, so to find a skyline community, the same procedure as S2 can be applied to calculate the maximum f2The value is denoted as f2All the sub-k-cores contained in H are derived from H2The result of the representation k-core must be one (f)1(H1)，f2(H1) Skyline community of, wherein f1(H1)＝f1*，f2(H1)＝f2Due to f2Is the largest of all current k-cores, so no other k-core can dominate it in the 2 nd dimension, f1All have the same f2The value of k-core is the largest and therefore there is no k-core that dominates it, which must be a skyline community since the previous recursion process ensured that the final k-core was the largest;
s3, then passing through the limit f1And f2Further calculating other skyline communities, and according to a calculation procedure similar to S2, refining the previous constraints, wherein the 2 nd dimension has a value greater than f2, and the 1 st dimension has a value greater than f1, because nodes with a value of no greater than f1 in the 1 st dimension and nodes with a value of no greater than f2 in the 2 nd dimension cannot be included in the undiscovered skyline communities;
s4, when d is 3, it is necessary to fix a node u first and find out all f on d-th dimension3The value is found by calling the 2 nd dimension algorithm to each f3Skyline community of 2 dimensions of value, finally f1、f2And f3The combination is 3-dimensional skyline community, and for 3-dimensional skyline community, the algorithm is based on a dimensionality reduction thought and comprises the following three steps:
s51, first, derive all possible f that skyline community may possess in dimension 33A value;
s52, secondly, for each possible f3Value (in f)3Representation), we find x1And x2All 2D skyline communications in a dimension, let f be3Value equal to f3Herein, skyline communities based on the 1 st and 2 nd dimensions are referred to as 2D skylinecocommunities, while all skyline communities based on three dimensions are referred to as 3D skyline communities;
s53, finally, for all possible f3Combining the values to generate the skyline community, calling a traditional skyline algorithm to determine all 3D skyline communities, and setting F3Is all possible f3A simple solution to the set of values, for S51, is to put F3Set as all x in G3Set of node values (x)3Representing the 3 rd dimension of the node) because f of all skyline communities3The value must be acquired from the set of all F3 node values, and S52 may be performed in such a manner that all x' S are deleted3Value less than f3Node of x, fixing node u as xu3＝f3(a fixed node indicates that the node cannot be deleted by the algorithm), it should be noted that there is only one xu of the node u3＝f3Is fixed because, according to the assumptions, all x3The values form a total order using the constraint I ═ x3≥f3The 2Dskyline community algorithm is called to calculate x by the fixed point set F ═ u ═ and the fixed point set F ═ u }1And 2D skyline community in the x2 dimension, it can be easily seen that the final community is2D skylinecommunity(x1And x2Dimensionally), f3Value equal to f3*；
S6, when d is larger than or equal to 3, the main difference is that the skyline community of (d-1) dimension is calculated by recursively calling, when d is 3, the recursive process is terminated, because the 3 rd dimension algorithm is called to calculate the 3 rd dimension skyline community, and finally f is calculated1、f2、f3Combining with skyline community of dimension (d-1), i.e. finding F3Is all possible f3A simple solution to the set of values, for S51, is to put F3Set as all x in G3Set of node values (x)3Representing the 3 rd dimension of the node) because f of all skyline communities3The value must be acquired from the set of all F3 node values, and S52 may be performed in such a manner that all x' S are deleted3Value less than f3Node of x, fixing node u as xu3＝f3(a fixed node indicates that the node cannot be deleted by the algorithm), it should be noted that there is only one xu of the node u3＝f3Is fixed because, according to the assumptions, all x3The values form a total order using the constraint I ═ x3≥f3The 2D skyline community algorithm is called to calculate x by the fixed point set F ═ u ═ and the fixed point set F ═ u }1And 2D skyline community in the x2 dimension, it can be easily seen that the final community is 2Dskyline community (x1And x2Dimensionally), f3Value equal to f3*。
Referring to fig. 2, it can be seen that 6 nodes in the graph each have 3 values in three different dimensions, and if k is 2, then H1 ═ V1, V2, and V3 are skyline communities with a value of f (H)1) (8, 14, 3) because there is no 2-core that can dominate it, and it is also the largest subgraph that satisfies the cohesiveness and skyline properties;
likewise, H2＝{V2，V4，V5，V6Is a skyline community, f (H)2) (6, 8, 4) subfigure H3＝{V4，V5V6 is not an skyline immunity because it is contained in H2＝{V2，V4，V5，V6In the f value and H of the community3The same; subfigure H4＝{V2，V3，V4，V5，V6Nor is skyline community because f (H)4) Is (6, 8, 3) is composed of H1And H2And (4) leading.
Compared with the related art, the method for discovering the densely connected sub-networks by the multi-value attribute graph structure has the following beneficial effects:
the invention discovers densely connected sub-network technology and framework by designing a multi-value attribute graph structure, is mainly used for detecting interested communities of each node in a multi-value network and associated with d number of value attributes, can find out sub-graphs with close connection, can consider a plurality of attributes while ensuring close connection, meanwhile, the communities identified by the model constructed by the invention cannot be dominated by other communities in the d-dimensional attribute space, further capturing all interesting communities in the d-dimensional attribute space to the maximum extent, wherein the model adopts k-core and skyline, utilizes the characteristics of the real world network, the influence of a plurality of factors can be considered simultaneously, and different from the prior scheme, the algorithm considers the attribute values of a plurality of nodes, the method and the device can search various attribute nodes in the multi-value attribute graph, and have better application value to a certain extent.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (9)
1. A method for discovering densely connected sub-networks by a multi-valued attribute graph structure, comprising the steps of:
s1, reading a multi-value attribute graph G, limiting I, fixing a node set F, dimension d and influence F;
s2, according to the limitation I, deleting none in the graphCalculating the maximum connection k-core subgraph H in the graph and calculating the maximum value f of H in the 1 st dimension1；
S3, passing through the maximum value f in the 1 st dimension1Further limiting accurately, calculating the maximum value f of 2 nd dimension2Obtaining a skyline community;
s4, then passing through the limit f1And f2Further calculating other skyline communities;
s5, when d is 3, it is necessary to fix a node u first and find out all f on d-th dimension3The value is found by calling the 2 nd dimension algorithm to each f3Skyline community of 2 dimensions of value, finally f1、f2And f3Merging to obtain 3-dimensional skyline community;
s6, when d is larger than or equal to 3, the main difference is that the skyline community of (d-1) dimension is calculated by recursively calling, when d is 3, the recursive process is terminated, because the 3 rd dimension algorithm is called to calculate the 3 rd dimension skyline community, and finally f is calculated1、f2、f3And (d-1) the skyline community is combined to obtain the demand.
2. The method of claim 1, wherein when calculating k-core subgraph H and maximum f in S2, calculating maximum f in dimension 1 of FIG. G1Is marked as f in all the maximum connection subgraphs k-core1The value of 1 st dimension in a maximal connected subgraph k-core subgraph H is f1By recursively deleting node values less than f1Nodes until no k-core exists in the graph.
3. The method for discovering the densely connected sub-networks according to the multi-value property graph structure of claim 1, wherein the very big connection sub-graph k-core H in S2 may not be a skyline community because H' may have the same f1Value, but f2CommunnityH 'with a value greater than H, but such group H'Must be contained in H because of its f1The value is the same as H, which is the largest of all k-cores.
4. The method for discovering densely connected sub-networks according to claim 1, wherein in order to find a skyline community in S3, the same steps as in S2 can be applied to calculate the maximum f2The value is denoted as f2All the sub-k-cores contained in H are derived from H2The result of the representation k-core must be one (f)1(H1)，f2(H1) Skyline community of, wherein f1(H1)＝f1*，f2(H1)＝f2Due to f2Is the largest of all the current k-cores, so no other k-core can dominate it in the 2 nd dimension.
5. The method for discovering densely connected sub-networks according to claim 1, wherein the other skyline community computation in S4 specifically comprises the steps of refining the previous constraints according to a computation step similar to S1, wherein the value of dimension 2 is greater than f2, and the value of dimension 1 is greater than f1, because nodes with dimension 1 no greater than f1 and nodes with dimension 2 no greater than f2 cannot be included in the undiscovered skyline community.
6. The method for discovering densely connected sub-networks according to the multi-value attribute graph structure of claim 1, wherein f in S31All have the same f2The value of k-core is the largest and therefore there is no k-core that dominates it, which must be a skyline community since the previous recursion process ensured that the final k-core was the largest.
7. The method for discovering densely connected sub-networks according to claim 1, wherein the algorithm for skyline communication with 3 dimensions in S5 is based on a dimension reduction idea, which comprises the following three steps:
s51, first, derive all possible f that skyline community may possess in dimension 33A value;
s52, secondly, for each possible f3Value (in f)3Representation), we find x1And x2All 2D skyline communications in a dimension, let f be3Value equal to f3Herein, skyline communities based on the 1 st and 2 nd dimensions are referred to as 2D skylinecocommunities, while all skyline communities based on three dimensions are referred to as 3D skyline communities;
s53, finally, for all possible f3And combining the generated skyline communities, and calling a traditional skyline algorithm to determine all the 3D skyline communities.
8. The method for discovering the densely connected sub-networks according to the multi-value attribute graph structure of claim 7, wherein F is set in S533Is all possible f3A simple solution to the set of values, for S51, is to put F3Set as all x in G3Set of node values (x)3Representing the 3 rd dimension of the node) because f of all skyline communities3The value must be acquired from the set of all F3 node values, and S52 may be performed in such a manner that all x' S are deleted3Value less than f3Node of x, fixing node u as xu3＝f3(a fixed node indicates that the node cannot be deleted by the algorithm), it should be noted that there is only one xu of the node u3＝f3Is fixed because, according to the assumptions, all x3The values form a total order using the constraint I ═ x3≥f3The 2D skyline community algorithm is called to calculate x by the fixed point set F ═ u ═ and the fixed point set F ═ u }1And 2D skyline community in the x2 dimension, it can be easily seen that the final community is 2D skyline community (x1And x2Dimensionally), f3Value equal to f3*。
9. The method for finding densely connected sub-networks according to claim 1, wherein in said S6, for skyline communications with dimension greater than 3, the general procedure of changing 3-dimensional skyline communications to more dimensions is very similar to 3-dimensional one, with the main difference that the algorithm recursively calls itself with parameter D-1 to calculate (D-1) dimension skyline communications when D is 3, the recursive procedure terminates because 3-dimensional algorithm is called to calculate 3D skyline communications.
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Application publication date: 20211109 |
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