CN103729467A - Community structure discovery method in social network - Google Patents

Community structure discovery method in social network Download PDF

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CN103729467A
CN103729467A CN201410020036.6A CN201410020036A CN103729467A CN 103729467 A CN103729467 A CN 103729467A CN 201410020036 A CN201410020036 A CN 201410020036A CN 103729467 A CN103729467 A CN 103729467A
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苏畅
王裕坤
贾文强
余跃
吴琪
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Abstract

The invention discloses a community structure discovery method in a social network, and belongs to the technical field of a network. The method comprises the steps of I. converting the social network into an adjacent matrix form, judging a corresponding edge as 1 if an edge exists between two nodes, otherwise judging to be 0; II. processing the adjacent matrix depending on a random walk theory to obtain a new node degree P-degree and an edge weight P-weight; III. obtaining a dominant node in the social network depending on the new node degree P-degree; and IV. generating a sub community depending on the dominant node, and implementing community discovery through a series of operations on the sub community. The method disclosed by the invention can effectively identify a community structure in the social network, and simultaneously compare the method with some classical community discovery algorithms such as Newman algorithm, and good performance is shown on a modularity index. The method disclosed by the invention has great significance in follow-up community network practice.

Description

Community structure discover method in a kind of social networks
Technical field
The invention belongs to networking technology area, relate to the community structure discover method in a kind of complicated social networks.
Background technology
In actual life, the system of many complexity or the form appearance with complex network, or can be converted into complex network, and such as social relation network, paper cooperative network, Computer Virus Spread network, Facebook network, QQ circle of friends etc.Community discovery is exactly to survey and disclose community structure intrinsic in complex network.It is used to help people to understand the function in complex network, finds to be hidden in the rule in complex network, and the behavior of prediction complex network.Since Girvan and Newman propose GN algorithm so far, the method that new theory is new emerges in an endless stream.The application of community discovery related algorithm is also constantly emerged in large numbers.
Except some classical community discovery algorithms, also have some algorithms in community discovery, also can obtain reasonable division effect, for example, the method that realizes community discovery in community network that the people such as Han Yi, Jia Yan proposes (patent No.: 201110103491.9, open day: 2012.05.16); The community discovery method based on random walk that the people such as Lin Zhiting, Wu Xiulong proposes (patent No.: 201110177783.7, open day: 2013.01.02); A kind of community discovery method that the people such as Xu Bingying, Han Weihong proposes and system (patent No.: 201310201298.8, open day: 2013.09.25) etc.In addition, the people such as Zhang Lu, Cai Wandong propose social networks leader of opinion recognition methods (patent No.: 201310028159.X, open day: 2013.05.22); The people such as Cai Lin, Cai Wandong has proposed the microblogging network leader of opinion recognition methods (patent No.: 201310027808,2013.06.05) open day: good elaboration has all been done in identification and the effect to leader's node such as, but yet exists some shortcomings about the identification of leader's node.
Based on some above-mentioned community discovery algorithms, although can obtain corresponding community structure, but when weighing using modularity as standard, still exist some shortcomings, the present invention proposes a kind of community discovery algorithm based on leader's node, be intended to better obtain the community structure in social networks, special using modularity as criterion in the situation that, can obtain higher modularity value, when the present invention tests in actual classic network data centralization, algorithm performance stability and high efficiency, algorithm is had very important significance and wide application prospect for follow-up social networks analysis.
Summary of the invention
In view of this, the object of the present invention is to provide the community structure discover method in a kind of social networks, the method is to utilize the thought of random walk to enter adjacency matrix is processed, obtain new node number of degrees P-degree and limit weights-weight, according to new node number of degrees P-degree, can obtain the leader's node in social networks, based on leader's node, generate sub-community, by the sequence of operations of antithetical phrase community, carry out community discovery.
For achieving the above object, the invention provides following technical scheme:
A community structure discover method in social networks, comprises the following steps: step 1: social networks is converted to adjacency matrix form, if there is limit between two nodes, so corresponding element is 1, otherwise is 0; Step 2: utilize random walk theory to process adjacency matrix, obtain new node number of degrees P-degree and limit weights P-weight; Step 3: obtain the leader's node in social networks according to new node number of degrees P-degree; Step 4: generate sub-community based on leader's node, and carry out community discovery by the sequence of operations of antithetical phrase community.
Further, in step 2, utilize the corresponding adjacency matrix of random walk theoretical treatment social networks, by new node number of degrees called after P-degree, the weights called after P-weight on new limit; The basis of leader's node is the value of P-degree (i); According to original matrix A, obtain transition matrix P, its element representation is P ij=A ij/ k i, wherein k ifor the number of degrees of node i; Meanwhile, according to transition matrix P, obtain P t, its element P ij tit is a random walk person goes to node j through t step probability from node i; Matrix PF is used for representing the matrix PF=P* θ that finally obtains 1+ P 2* θ 2+ P 3* θ 3...+P t* θ t, Parameters in Formula θ 1, θ 2, θ 2... θ t, 0≤θ i≤ 1,1≤i≤t, represents different transition matrixs to give different weights; According to transition matrix, PF obtains P-degree, (P-degree (i))=PF (i, i).
Further, in step 3, first the node in social networks is carried out to descending sort according to the value of P-degree (i), interstitial content is n, threshold value using the residing position of n/4 element in descending list as leader's node, then carries out the selection of leader's node with this; Confirm, after leader's node, using leader's node as core, the node being directly connected with leader's node to be merged, begin to take shape sub-community structure.
Further, in step 4, utilize statistical model according to the order of sequence to remain the processing of adding of node and sub-community lap; With cos-similarity, represent the weights on limit, cos - similarity ( v i , v j ) = ( v i , v j ) / ( ( v i , v i ) * ( v j , v j ) ) , Wherein v iand v j, the capable and j every trade vector of the i of representing matrix PF; The formula that obtains P-weight (i, j) according to the value of cos-similarity is as follows: (P-weight (i, j))=w* (cos-similarity), and wherein w is weights; The C of antithetical phrase community t, node i is with respect to C tstatistical value be
Figure BDA0000457880180000022
different δ is calculated in different sub-communities t, δ=max (δ 1, δ 2δ 3... δ t), if δ kmaximum, node i just belongs to k Ge Zi community so.
Further, in step, need less community to be incorporated in larger community, adopt following steps to process: to define little community concept, min_length=aver_length (a with min_length s1, a s2... a st)/4, wherein, aver_length (a s1, a s2... a st) represent Shi Ge community average nodal number, for intercommunal merging, adopt following formula to carry out: a sk=max_link (link (a s1, a sk), link (a s2, a sk) ... link (a st, a sk)), link (a st, a sk) that represent is a st, a skthe number on the limit connecting, tries to achieve a skthat community of counting maximum with all community's fillets be exactly will with a skthe community merging, obtains corresponding community structure after having merged.
Beneficial effect of the present invention is: community discovery method provided by the invention, how effectively to have solved more effective discovery leader node, and by leader's node of finding the problem for community discovery, can identify efficiently the community structure in social networks; Simultaneously by community discovery algorithm classical with some this method as compared with Newman algorithm, in modularity index, have better performance.The present invention is had great significance for follow-up social networks practice.
Accompanying drawing explanation
In order to make object of the present invention, technical scheme and beneficial effect clearer, the invention provides following accompanying drawing and describe:
Fig. 1 is the macro flow chart of the method for the invention;
Fig. 2 is that this method is applied to Karate fight club network topology schematic diagram;
Fig. 3 is that this method is applied to Dolphins relational network topology schematic diagram;
Fig. 4 is that this method is applied to AmericanFootball club network topology schematic diagram.
Embodiment
Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.
Overall technology embodiment of the present invention is as follows:
1. test of heuristics data set
In the present embodiment, the data set adopting has three, is respectively Karate club network, Dol phins relational network and AmericanFootball network, its Network data set is described below:
1) Karate fight club network
Phase early 1970s, Wayne Zachary observes karate club with the time of 2 years, and Zhe Jia karate club is a university from the U.S..Wayne Zachary has constructed clubbite's network, and this network is to form according to the social relationships between member in club.But in his fact-finding process, found this club internal problem, about whether improving charge mark standard, between their supervisor and principal, suggestion has produced difference exactly.Result, part member is taken away and has been organized into a new club by coach, and remaining member stays original club, and finally Zachary karate club splits into Liao Liangge little club, one with headed by principal, and another is that to be responsible for be core.Shown in figure mono-is two different corporations that Zachary karate club is divided into, and comprises altogether 34 members and 78 limits, and each node has represented respectively each member in the little club after division.In the community structure of complex network is analyzed, Zachary network has been widely applied in research network community structure partitioning algorithm, and what we used in the present invention is exactly this data set.We are by the algorithm application in the present invention in this data set, and the network topology structure obtaining as shown in Figure 2.
2) Dolphins relational network
In 1994, to calendar year 2001, D.Lusseau studied time of 7 years to dolphin and has obtained Dolphins relational network.This network comprises altogether 62 nodes, wherein each node represents a dolphin, and two dolphins have intimate relation, just connecting a limit between the node of these two dolphin representatives, we are by algorithm application of the present invention in this data set, and the network topology structure obtaining as shown in Figure 3.
3) AmericanFootball network
An American university tissue 2000 season football connect the pool match of racing season.Wherein each node in network represents a football team, and has match between the Shi Liangge team that company limit between node represents.And current all matches can be divided into 12 groups, each team is many with the team's match number of times that belongs to same a small group, about 7; And relative with the match that does not belong to a group less, about 4, so a network with community structure has been formed by these teams.Algorithm by us divides American university football match network, and a network with community structure has been formed by these teams.We are by algorithm application of the present invention in this data set, and the network topology structure obtaining as shown in Figure 4.
2. realize the community discovery algorithm based on leader's node
In order to find leader's node and the sub-community in social networks, first utilize random walk to process adjacency matrix, obtain the leader's node in community network, using leader's node as core, build sub-community, then by residue the adding of node, and sub intercommunal merging obtains corresponding community structure.
According to the corresponding adjacency matrix of social networks, obtain leader's node concrete steps as follows:
Step 1: obtain P-degree by the relative adjacency matrix of social networks is carried out to pre-service.According to original matrix A, obtain transition matrix P, its element can be expressed as P ij=A ij/ k i, wherein k ifor the number of degrees of node i.In this simultaneously, according to transition matrix, P obtains P t, its element representation P ij trepresent that a random walk person goes to the probability of node j through t step from node i.Matrix PF is used for representing the matrix PF=P* θ that finally obtains 1+ P 2* θ 2+ P 3* θ 3...+P t* θ t, Parameters in Formula θ 1, θ 2, θ 2... θ t, 0≤θ i≤ 1,1≤i≤t, represents different transition matrixs to give different weights.According to transition matrix, PF obtains P-degree, (P-degree (i))=PF (i, i).
Step 2: utilize P-degree to obtain leader's node and sub-community.First the node in social networks is carried out to descending sort according to the value of P-degree (i), interstitial content is n, and the threshold value using the residing position of n/4 element in descending list as leader's node, then carries out the selection of leader's node with this.Confirm, after leader's node, using leader's node as core, the node being directly connected with leader's node to be merged, begin to take shape sub-community structure.
After obtaining leader's node and correlator community, remaining work is exactly the value that obtains P-weight according to adjacency matrix, according to the value of P-weight, the residue node in social networks is added, finally the sub-community obtaining is further merged and obtains final community structure.Its concrete steps are as follows:
Step 1: the value and the residue node that obtain P-weight according to adjacency matrix add.We represent the weights on limit with cos-similarity, cos - similarity ( v i , v j ) = ( v i , v j ) / ( ( v i , v i ) * ( v j , v j ) ) , Wherein v iand v j, the capable and j every trade vector of the i of representing matrix PF.The formula that obtains P-weight (i, j) according to the value of cos-similarity is as follows: (P-weight (i, j))=w* (cos-similarity), wherein w is weights.The C of antithetical phrase community t, node i is with respect to C tstatistical value be different δ is calculated in different sub-communities t, δ=max (δ 1, δ 2δ 3... δ t), if δ kmaximum, node i just belongs to k Ge Zi community so.
Step 2: sub-community further merges and obtains community structure.There is multinode overlapping phenomenon in the community structure obtaining now, and the difference of intercommunal interstitial content sometimes can be very large, less community need to be incorporated in larger community, define little community concept, min_length=aver_length (a with min_length s1, a s2... a st)/4, aver_length (a s1, a s2... a st) represent Shi Ge community average nodal number, as for intercommunal merging, adopt following mathematical formulae a sk=max_link (link (a s1, a sk), link (a s2, a sk) ... link (a st, a sk)), link (a st, a sk) that represent is a st, a skthe number on the limit connecting, tries to achieve a skthat community of counting maximum with all community's fillets be exactly will with a skthe community merging.After having merged, obtain corresponding community structure.
Finally explanation is, above preferred embodiment is only unrestricted in order to technical scheme of the present invention to be described, although the present invention is described in detail by above preferred embodiment, but those skilled in the art are to be understood that, can to it, make various changes in the form and details, and not depart from the claims in the present invention book limited range.

Claims (5)

1. the community structure discover method in social networks, is characterized in that: comprise the following steps:
Step 1: social networks is converted to adjacency matrix form, if there is limit between two nodes, so corresponding element is 1, otherwise is 0;
Step 2: utilize random walk theory to process adjacency matrix, obtain new node number of degrees P-degree and limit weights P-weight;
Step 3: obtain the leader's node in social networks according to new node number of degrees P-degree;
Step 4: generate sub-community based on leader's node, and carry out community discovery by the sequence of operations of antithetical phrase community.
2. the community structure discover method in a kind of social networks according to claim 1, it is characterized in that: in step 2, utilize the corresponding adjacency matrix of random walk theoretical treatment social networks, by new node number of degrees called after P-degree, the weights called after P-weight on new limit; The basis of leader's node is the value of P-degree (i); According to original matrix A, obtain transition matrix P, its element representation is P ij=A ij/ k i, wherein k ifor the number of degrees of node i; Meanwhile, according to transition matrix P, obtain P t, its element P ij tit is a random walk person goes to node j through t step probability from node i; Matrix PF is used for representing the matrix PF=P* θ that finally obtains 1+ P 2* θ 2+ P 3* θ 3+ P t* θ t, Parameters in Formula θ 1, θ 2, θ 2... θ t, 0≤θ i≤ 1,1≤i≤t, represents different transition matrixs to give different weights; According to transition matrix, PF obtains P-degree, (P-degree (i))=PF (i, i).
3. the community structure discover method in a kind of social networks according to claim 2, it is characterized in that: in step 3, first the node in social networks is carried out to descending sort according to the value of P-degree (i), interstitial content is n, threshold value using the residing position of n/4 element in descending list as leader's node, then carries out the selection of leader's node with this; Confirm, after leader's node, using leader's node as core, the node being directly connected with leader's node to be merged, begin to take shape sub-community structure.
4. the community structure discover method in a kind of social networks according to claim 3, is characterized in that: in step 4, utilize statistical model according to the order of sequence to remain the processing of adding of node and sub-community lap; With cos-similarity, represent the weights on limit, cos - similarity ( v i , v j ) = ( v i , v j ) / ( ( v i , v i ) * ( v j , v j ) ) , Wherein v iand v j, the capable and j every trade vector of the i of representing matrix PF; The formula that obtains P-weight (i, j) according to the value of cos-similarity is as follows: (P-weight (i, j))=w* (cos-similarity), and wherein w is weights; The C of antithetical phrase community t, node i is with respect to C tstatistical value be
Figure FDA0000457880170000012
different δ t, δ=max (δ are calculated in different sub-communities 1, δ 2δ 3... δ t), if δ kmaximum, node i just belongs to k Ge Zi community so.
5. the community structure discover method in a kind of social networks according to claim 4, it is characterized in that: in step, need less community to be incorporated in larger community, adopt following steps to process: to define little community concept, min_length=aver_length (a with min_length s1, a s2... a st)/4, wherein, aver_length (a s1, a s2... a st) represent Shi Ge community average nodal number, for intercommunal merging, adopt following formula to carry out: a sk=max_link (link (a s1, a sk), link (a s2, a sk) ... link (a st, a sk)), link (a st, a sk) that represent is a st, a skthe number on the limit connecting, tries to achieve a skthat community of counting maximum with all community's fillets be exactly will with a skthe community merging, obtains corresponding community structure after having merged.
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CN104657901A (en) * 2015-01-14 2015-05-27 重庆邮电大学 Community discovery method based on label propagation in random walk
CN105095403A (en) * 2015-07-08 2015-11-25 福州大学 Parallel community discovery algorithm based on mixed neighbor message propagation
CN107993156A (en) * 2017-11-28 2018-05-04 中山大学 A kind of community discovery method based on social networks digraph
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CN105095403A (en) * 2015-07-08 2015-11-25 福州大学 Parallel community discovery algorithm based on mixed neighbor message propagation
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CN107993156A (en) * 2017-11-28 2018-05-04 中山大学 A kind of community discovery method based on social networks digraph
CN108376371A (en) * 2018-02-02 2018-08-07 众安信息技术服务有限公司 A kind of internet insurance marketing method and system based on social networks
CN109828998B (en) * 2019-01-14 2021-05-25 中国传媒大学 Grouping method and system based on core group mining and opinion leader identification results
CN109828998A (en) * 2019-01-14 2019-05-31 中国传媒大学 Grouping method and system based on core population excavation and leader of opinion's recognition result
CN112269922A (en) * 2020-10-14 2021-01-26 西华大学 Community public opinion key character discovery method based on network representation learning
CN113723583A (en) * 2021-08-28 2021-11-30 重庆理工大学 Multi-domain network community discovery method based on discrete time quantum migration
CN113723583B (en) * 2021-08-28 2023-07-21 重庆理工大学 Multi-domain network community discovery method based on discrete time quantum migration

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