CN113536052A - Method for searching personalized influence community in large network based on k-edge connected component - Google Patents
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Abstract
The invention discloses a method for searching a personalized influence community in a large network based on k-edge connected components. Traditional social searches ignore the need for personalization. The invention provides a new model, namely a k-edge connected component (PIKE) model of personalized influence. It measures the cohesiveness of subgraphs using a k-edge connected component model and attempts to find influential communities from a set of query nodes. It needs to satisfy four conditions: contains all given query nodes; satisfying k edge connected component constraint; the influence of the subgraph is greatest; is extremely large, i.e., any hypergraph thereof cannot satisfy the first three conditions. In order to solve the problem and quickly find the PIKE in a large network, the invention provides a query method based on the dichotomy. The method for searching the personalized influence community in the large network based on the k-edge connected component has great benefit for the research of the social network.
Description
Technical Field
The invention belongs to the technical field of graph data mining, and particularly relates to a method for searching a personalized influence community in a large network based on k-edge connected components.
Background
Community search is a fundamental problem in social network analysis. The purpose of community search is to identify important communities (i.e., cohesive subgraphs) containing querying users, which is an important tool for personalized applications such as friend recommendation, product promotion, and the like. Many cohesive subgraph models have been proposed in current research, such as k-kernels, k-trusses, and k-edge connected components. In a social network, a user is typically associated with a weight that represents their impact in the network. The influence value of a community is defined as the minimum weight of the nodes in the community. In recent years, the problem of influence community detection has attracted a lot of attention. However, there is currently no intention to investigate the need to take into account personalization. The invention provides a personalized influence community searching problem based on k-edge connected components, and aims to find out a corresponding personalized influence community by continuously deleting nodes influencing community influence. In order to better process a large network, the invention provides a novel algorithm based on the dichotomy idea, so that the nodes can be deleted in batches, and the search time is obviously shortened. The method for searching the personalized influence community in the large network based on the k-edge connected component has great benefit for the research of the social network.
Disclosure of Invention
In order to meet the demand of personalization, the invention provides a new problem, namely personalized influence k-edge connected component (PIKE) search for finding personalized influence communities in the social network. The method measures the cohesion of the subgraph by adopting a k-edge connected component model widely applied to social network analysis. Given a graph G to be queried and a query node set Q, the personalized influence community PIKE is a subgraph with the maximum influence value in the graph G, and four conditions are required to be met: 1) all query nodes in Q are included; 2) satisfying k edge connected component constraint, namely removing any k-1 edge in a certain graph, and then any two nodes in the graph are still reachable; 3) the influence value of the subgraph is maximum; 4) is extremely large, i.e., any hypergraph thereof cannot satisfy the first three conditions.
The method is based on the following lemma: for the two subgraphs G1 and G2 of graph G, where subgraph G1 contains subgraph G2 and subgraph G1 is the union of subgraph G2 and node a, if the influence value of node a is less than that of subgraph G2, then the influence value of subgraph G1 is also less than that of subgraph G2;
the method comprises the following steps:
step one, calculating all k-edge connected components in a graph G;
step two, finding out a k-edge connected component containing all the query nodes in Q: if Q is not contained in any k-edge connected component, returning an error report; otherwise, sorting all the remaining nodes with the influence values smaller than the minimum influence value of the query node in the Q in the k-edge connected component containing the Q in ascending order according to the influence values and storing the nodes in a set S, and if the S is empty, returning the current k-edge connected component;
and step three, deleting the nodes in batches based on the dichotomy: iteratively dividing the nodes in S into two sets D1 and D2; d1 contains the nodes of the first half of S, i.e. the nodes with small influence value, and D2 contains the rest of other nodes; according to the theory, all nodes in D1 are removed from the current k-edge connected component, all k-edge connected components in a subgraph formed by the rest nodes in the k-edge connected component are calculated and returned, if the returned result contains the k-edge connected component containing Q, an S set corresponding to the k-edge connected component is calculated through the second step, and the third step is repeatedly executed; if the returned result does not contain the k-side connected component of Q, if the node number in D1 is not 1, step three is repeatedly executed on the k-side connected component of D1, which is not removed, with D1 as a new S set, and if the node number in D1 is 1, it means that the k-side connected component of D1 is not removed, and the final sub-graph PIKE is output.
Further, in the first step, the method for calculating the k-edge connected component specifically includes: firstly, creating an empty list L and randomly selecting a node from an original graph G to be placed in the L; the following is then performed iteratively:
putting the node which is originally not in the L and can form the most number of edges with all nodes in the L in the graph G into the tail part of the L; after each new node is added into the L, executing corresponding query and update operations;
the query operation is: suppose a newly added node is u; before u joins L, the latest joining node in L is v; if u and v are connected in a subgraph formed by the nodes in the L at the moment, carrying out updating operation;
the update operation is: merging u and v into a super node, and treating the super node as a node in subsequent operation;
continuing the process until all nodes in the graph G are added into the L and executing corresponding query and update operations;
for the two nodes u 'and v' that last added to L in graph G, if u 'and v' are not k-connected, the last added node in L is removed from L;
and repeating all the steps for the current graph containing the super nodes, wherein finally the subgraph formed by all the nodes in each super node is a k-edge connected component in the original graph G.
The invention also provides a computer device, which comprises a memory and a processor, wherein the memory stores computer readable instructions, and the computer readable instructions, when executed by the processor, cause the processor to execute the steps of the method for searching the personalized influence community in the large network based on the k-edge connected component.
The present invention also provides a storage medium storing computer-readable instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of the above method for searching a personalized influence community in a large network based on k-edge connected components.
The invention has the beneficial effects that: in a social network, a user is typically associated with a weight that represents their value of influence in the network. The purpose of the influence community detection is not only to find out the communities with cohesiveness, but also to require a larger influence value. Wherein the influence value of the community refers to the minimum influence value of all nodes in the community. While the k-edge connected component is a common model to measure community cohesion. Therefore, the invention provides a large-scale network personalized influence community search problem based on k-edge connected components, and aims to identify communities containing given query nodes. In addition, in order to reduce the cost for processing a large network, the invention develops an efficient query method based on the dichotomy, so that the community with the largest influence value containing the specified node can be quickly found in the large network, and the search cost is effectively reduced. Therefore, the method for searching the personalized influence community in the large network based on the k-edge connected component has great benefit for the research of the social network.
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FIG. 1 is a flow chart of a method for searching a personalized influence community in a large network based on k-edge connected components according to the present invention;
FIG. 2 is a detailed implementation flowchart of the personalized influence community binary search provided in the embodiment of the present invention;
FIG. 3 is a schematic diagram of a raw influence network;
FIG. 4 is a schematic diagram of the original force network after computing the 2-edge connected component;
5-7 are schematic diagrams of a binary search of a 2-edge connected component containing a gray target node;
FIG. 8 is a diagram of a personalized influential community after conducting a binary search.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
The application provides a method for searching an individual influence community in a large network based on k-edge connected components, a graph G to be queried and a query node set Q are given, an individual influence community PIKE is a subgraph with the maximum influence value in the graph G, and four conditions are required to be met: 1) all query nodes in Q are included; 2) satisfying k edge connected component constraint, namely removing any k-1 edge in a certain graph, and then any two nodes in the graph are still reachable; 3) the influence value of the subgraph is maximum; 4) is extremely large, i.e., any hypergraph thereof cannot satisfy the first three conditions. The following describes the implementation of the method of the present invention in detail, as shown in fig. 1 and 2.
The method is based on the following lemma:
for the two subgraphs G1 and G2 of graph G, where subgraph G1 contains subgraph G2 and subgraph G1 is the union of subgraph G2 and node a, if the influence value of node a is less than that of subgraph G2, then the influence value of subgraph G1 is also less than that of subgraph G2.
The method comprises the following steps:
step one, calculating all k-edge connected components in a graph G;
in one embodiment, the method for calculating the k-edge connected component specifically includes: firstly, creating an empty list L and randomly selecting a node from an original graph G to be placed in the L; the following is then performed iteratively:
putting the node which is originally not in the L and can form the most number of edges with all nodes in the L in the graph G into the tail part of the L; after each new node is added into the L, executing corresponding query and update operations;
the query operation is: suppose a newly added node is u; before u joins L, the latest joining node in L is v; if u and v are connected in a subgraph formed by the nodes in the L at the moment, carrying out updating operation;
the update operation is: merging u and v into a super node, and treating the super node as a node in subsequent operation;
continuing the process until all nodes in the graph G are added into the L and executing corresponding query and update operations;
for the two nodes u 'and v' that last added to L in graph G, if u 'and v' are not k-connected, the last added node in L is removed from L;
and repeating all the steps for the current graph containing the super nodes, wherein finally the subgraph formed by all the nodes in each super node is a k-edge connected component in the original graph G.
Step two, finding out a k-edge connected component containing all the query nodes in Q: if Q is not contained in any k-edge connected component, returning an error report; and if not, sorting and storing all the residual nodes with the influence values smaller than the minimum influence value of the query node in the Q in the set S according to ascending order of the influence values, and if the S is empty, returning the current k-edge connected component.
And step three, deleting the nodes in batches based on the dichotomy: iteratively dividing the nodes in S into two sets D1 and D2; d1 contains the nodes of the first half of S, i.e. the nodes with small influence value, and D2 contains the rest of other nodes; according to the theory, all nodes in D1 are removed from the current k-edge connected component, all k-edge connected components in a subgraph formed by the rest nodes in the k-edge connected component are calculated and returned, if the returned result contains the k-edge connected component containing Q, an S set corresponding to the k-edge connected component is calculated through the second step, and the third step is repeatedly executed; if the returned result does not contain the k-side connected component of Q, if the node number in D1 is not 1, taking D1 as a new S set, and repeatedly executing the step three on the k-side connected component without removing D1, if the node number in D1 is 1, the k-side connected component without removing D1 is the final subgraph PIKE, and outputting the final subgraph PIKE.
The following describes the implementation of the present invention by taking the graph to be queried originally as an example shown in fig. 3, wherein the nodes in dark gray represent the query node set Q, i.e., node 7, node 8 and node 9. FIG. 4 is a subgraph calculated by the k-edge connected component algorithm in step one, wherein the dotted lines represent nodes and edges filtered out because the condition is not satisfied, and the node 15 is deleted because the constraint of the k-edge connected component is not satisfied. Fig. 5 is a diagram showing the result after dividing nodes in ascending order of influence value of the nodes in step three, wherein the nodes in D1 are indicated by horizontal stripes, and the nodes in D2 are indicated by vertical stripes. Fig. 6 is a sub-graph of step three after all nodes in D1 are deleted using the bisection algorithm. Fig. 7 is a subgraph in which after the node in D1 is deleted, other nodes are deleted because the k-edge connected component constraint is not satisfied, and at this time, only node 6 is located at a point in the remaining graph that is smaller in weight than the node set Q, that is, only node 6 is located in S, and at this time, removing node 6 causes the query node to be deleted, so that the current operation is stopped and the result obtained in the previous process is returned. Fig. 8 shows the final result.
In addition, the invention downloads 3 real social network data sets from the data set website SNAP, and carries out extensive experiments based on the three data sets to evaluate the effectiveness and the high efficiency of the proposed method. To evaluate the performance of the proposed method, we performed experiments by varying the parameter k, the number of query nodes | Q | and the weight distribution ω of the query nodes. For each setting, we randomly generated 20 queries of non-null results and run the algorithm 10 times to report the average response time. All procedures were implemented in standard c + + and all experiments were performed on a PC equipped with an Intel i5-9600KF 3.7GHz CPU and 64GB main memory. Experiments show that compared with a baseline method, the method provided by the invention can achieve an acceleration ratio of 2 orders of magnitude.
In one embodiment, a computer device is provided, which includes a memory and a processor, the memory stores computer readable instructions, and when executed by the processor, the processor executes the steps of the method for searching a personalized influence community in a large network based on k-edge connected components in the embodiments.
In one embodiment, a storage medium storing computer-readable instructions is provided, which when executed by one or more processors, cause the one or more processors to perform the steps of the method for searching a personalized influence community in a large network based on k-edge connected components in the above embodiments. The storage medium may be a nonvolatile storage medium.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by associated hardware instructed by a program, which may be stored in a computer-readable storage medium, and the storage medium may include: read Only Memory (ROM), Random Access Memory (RAM), magnetic or optical disks, and the like.
The foregoing is only a preferred embodiment of the present invention, and although the present invention has been disclosed in the preferred embodiments, it is not intended to limit the present invention. Those skilled in the art can make numerous possible variations and modifications to the present teachings, or modify equivalent embodiments to equivalent variations, without departing from the scope of the present teachings, using the methods and techniques disclosed above. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.
Claims (4)
1. A method for searching a personalized influence community in a large network based on a k-edge connected component is characterized in that a graph G to be queried and a query node set Q are given, the personalized influence community PIKE is a subgraph with the maximum influence value in the graph G, and four conditions are required to be met: 1) all query nodes in Q are included; 2) satisfying k edge connected component constraint, namely removing any k-1 edge in a certain graph, and then any two nodes in the graph are still reachable; 3) the influence value of the subgraph is maximum; 4) is extremely large, i.e. any hypergraph thereof cannot satisfy the first three conditions;
the method is based on the following lemma: for the two subgraphs G1 and G2 of graph G, where subgraph G1 contains subgraph G2 and subgraph G1 is the union of subgraph G2 and node a, if the influence value of node a is less than that of subgraph G2, then the influence value of subgraph G1 is also less than that of subgraph G2;
the method comprises the following steps:
step one, calculating all k-edge connected components in a graph G;
step two, finding out a k-edge connected component containing all the query nodes in Q: if Q is not contained in any k-edge connected component, returning an error report; otherwise, sorting all the remaining nodes with the influence values smaller than the minimum influence value of the query node in the Q in the k-edge connected component containing the Q in ascending order according to the influence values and storing the nodes in a set S, and if the S is empty, returning the current k-edge connected component;
and step three, deleting the nodes in batches based on the dichotomy: iteratively dividing the nodes in S into two sets D1 and D2; d1 contains the nodes of the first half of S, i.e. the nodes with small influence value, and D2 contains the rest of other nodes; according to the theory, all nodes in D1 are removed from the current k-edge connected component, all k-edge connected components in a subgraph formed by the rest nodes in the k-edge connected component are calculated and returned, if the returned result contains the k-edge connected component containing Q, an S set corresponding to the k-edge connected component is calculated through the second step, and the third step is repeatedly executed; if the returned result does not contain the k-side connected component of Q, if the node number in D1 is not 1, taking D1 as a new S set, and repeatedly executing the step three on the k-side connected component without removing D1, if the node number in D1 is 1, the k-side connected component without removing D1 is the final subgraph PIKE, and outputting the final subgraph PIKE.
2. The method according to claim 1, wherein in the first step, the method for calculating the k-edge connected component specifically comprises: firstly, creating an empty list L and randomly selecting a node from an original graph G to be placed in the L; the following is then performed iteratively:
putting the node which is originally not in the L and can form the most number of edges with all nodes in the L in the graph G into the tail part of the L; after each new node is added into the L, executing corresponding query and update operations;
the query operation is: suppose a newly added node is u; before u joins L, the latest joining node in L is v; if u and v are connected in a subgraph formed by the nodes in the L at the moment, carrying out updating operation;
the update operation is: merging u and v into a super node, and treating the super node as a node in subsequent operation;
continuing the process until all nodes in the graph G are added into the L and executing corresponding query and update operations;
for the two nodes u 'and v' that last added to L in graph G, if u 'and v' are not k-connected, the last added node in L is removed from L;
and repeating all the steps for the current graph containing the super nodes, wherein finally the subgraph formed by all the nodes in each super node is a k-edge connected component in the original graph G.
3. A computer device comprising a memory and a processor, the memory having stored therein computer readable instructions which, when executed by the processor, cause the processor to perform the steps of the method of searching for personalized influence communities in a large network based on k-edge connected components as claimed in any one of claims 1, 2.
4. A storage medium storing computer readable instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of the method of searching for personalized influence communities in a large network based on k-edge connectivity components as claimed in any one of claims 1, 2.
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| US20130318092A1 (en) * | 2012-05-25 | 2013-11-28 | The Board of Trustees for the Leland Stanford, Junior, University | Method and System for Efficient Large-Scale Social Search |
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