CN103593800A - Community discovery method based on faction random walk - Google Patents

Community discovery method based on faction random walk Download PDF

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CN103593800A
CN103593800A CN201310518584.7A CN201310518584A CN103593800A CN 103593800 A CN103593800 A CN 103593800A CN 201310518584 A CN201310518584 A CN 201310518584A CN 103593800 A CN103593800 A CN 103593800A
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faction
community
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factions
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CN103593800B (en
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鲍亮
王焱楠
张珂
陈平
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Xidian University
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Abstract

本发明公开一种基于派系随机游走的社区发现方法，解决现有社区发现方法的结果不稳定、无法发现重叠社区和不同层次下的社区结构的问题。具体步骤包括：（1）从社会网络中找出极大派系；（2）处理多余的极大派系和孤立节点；（3）构造极大派系网络；（4）初始化紧密度矩阵；（5）找出每个极大派系所在的社区；（6）得到每个社区中的社会网络节点。本发明具有发现重叠社区和不同层次下的社区结构的能力，提高了社区发现结果的稳定性。

The invention discloses a community discovery method based on faction random walk, which solves the problems that the result of the existing community discovery method is unstable, overlapping communities and community structures at different levels cannot be found. The specific steps include: (1) find out the maximal clique from the social network; (2) deal with redundant maximal cliques and isolated nodes; (3) construct the maximal clique network; (4) initialize the closeness matrix; (5) Find out the community where each maximal faction is located; (6) Get the social network nodes in each community. The invention has the ability to discover overlapping communities and community structures under different levels, and improves the stability of community discovery results.

Description

Community discovery method based on factions' random walk
Technical field
The invention belongs to field of computer technology, further relate to a kind of community discovery method based on factions' random walk in data mining technology field.The overlapping community of the present invention in can discovering network and the community structure under different levels, and can improve the stability of community's result.
Background technology
Community discovery technology is that the community structure in discovering network is a fundamental research in complex network, by find community structure in complex network, and to take the network that these community structures are that unit forms be research object, the rule can be under significantly reducing research complexity containing in to network is studied discovery.
The patented technology that PLA University of Science and Technology for National Defense has " the community discovery method " (applying date: 2010.03.01 Granted publication number: disclose a kind of community discovery method CN102194149B).The method comprises: in a community network, according to the scale scope that will find community, delimit a region of search; Neighbor node array according to node in described region of search is done cut operator; A selected node in the residue node of the community network through cut operator, in the neighbor node of this node, searching for size is | the community of S|-1, after finding, by this node and the size searching, being | the community of S|-1 forms the community that will find, is added in result set; The left margin of described region of search is moved to the left, then in the region of search after expansion, re-executes abovementioned steps, until region of search reaches the minimum value of the scale that will find community.The deficiency that the method exists is that, because the neighbor node number according to node is done cut operator, the method cannot be found overlapping community.
The patent " the medicine Combo discovering method based on complex network model parallelization label propagation algorithm " of Nanjing University's application (application number: 201210111171.2 applyings date: open day of 2012.04.16 publication number: CN102663108A: 2012.09.12), disclose a kind of medicine Combo discovering method based on complex network model parallelization label propagation algorithm.The method comprises the steps: the networking stage: a) pre-service generates Chinese medicine data set, is formatted as text data; B) initial text data is disposed to Hadoop to platform; C) Chinese medicine network is set up in parallelization; D) finish.Excavation phase: a) obtaining step 1-c processes the Chinese medicine network text file generating; B) Chinese medicine network text file is disposed to the platform to Hadoop; C) implement parallelization label propagation algorithm and find medicine corporations; D) finish.The deficiency that the method exists is that, owing to adopting label propagation to carry out community discovery, the method cannot be found the community structure under different levels; Because label propagation exists instability, cause using the method to carry out the unstable result of community discovery.
Summary of the invention
The present invention is directed to above-mentioned the deficiencies in the prior art, proposed a kind of community discovery method based on factions' random walk.
The concrete thought that the present invention realizes is: first from community network, find out very big factions, then find out the community at each very big factions place, with the very big factions in each community of all community network node replacements in very big factions, overcome prior art and cannot find the shortcoming of overlapping community, made the present invention there is the ability of finding overlapping community.By changing the size of multi-scale parameters, obtain different community's Attraction Degree, thereby obtain the community structure under different levels, overcome the shortcoming that prior art can not obtain the community structure under different levels, make the present invention to there is the ability that can obtain the community structure under different levels.Calculate the random movement probability of very big factions to community, find out the community at each very big factions place, thereby obtain the community network node in each community, overcome the shortcoming of community's unstable result that prior art obtains, improved the stability of community discovery result.
The concrete steps that the present invention realizes comprise as follows:
(1) from community network, find out very big factions:
(2) process unnecessary very big factions and isolated node:
2a) optional very big factions in found out very big factions;
The node sum and the node in selected very big factions that 2b) compare in each very big factions are total, find out the very big factions that are greater than the node sum in selected very big factions;
2c) adopt degree of comprising value formula, calculate degree of the comprising value of the very big factions more than the node sum in selected very big factions with respect to node sum of selected very big factions;
2d) in judgement degree of comprising value, whether be greater than 0.75, if so, from found out very big factions set, delete selected very big factions, otherwise, retain selected very big factions, execution step 2e);
2e) judge that whether the very big factions in community network are all processed complete, if so, perform step 2f), otherwise, execution step 2a);
2f) travel through all very big factions, find out the isolated node not being included in any one very big factions;
2g) isolated node is joined in the very big factions that the neighbor node number that comprises isolated node is maximum;
(3) construct very big factions network:
3a) optional two very big factions in very big factions, adopt degree of overlapping formula, calculate the degree of overlapping of selected two very big factions;
Whether the degree of overlapping that 3b) judges every two very big factions has all been calculated, and if so, performs step 3c), otherwise, execution step 3a);
3c) degree of overlapping is greater than between two very big factions of 0.2 and sets up a limit, form very big factions network;
(4) initialization tight ness rating matrix:
4a) optional two very big factions in very big factions, adopt tight ness rating formula, calculate the tight ness rating of selected two very big factions;
Whether the tight ness rating that 4b) judges every two very big factions has all been calculated, if so, perform step (5), otherwise, execution step 4a);
(5) find out the community at each very big factions place:
5a) each very big factions is constructed respectively to an initial community for correspondence with it, in each initial community, only have very big factions;
5b) optional very big factions in very big factions, obtain community's set at the very big factions of the neighbours place of selected very big factions;
5c) calculate the community Attraction Degree of each community to selected very big factions in the set of community, neighbours very big factions place;
5d) calculate the random movement probability of selected very big factions to each community in the set of community, neighbours very big factions place, obtain largest random movement probability;
5e) the community from own place by selected very big factions, the community corresponding to largest random movement probability moves, and obtains society's area code at selected very big factions place in current iteration;
5f) all very big factions are judged whether to obtain society's area code at its place, if so, perform step 5g), otherwise, execution step 5b);
5g) to all very big factions, judge that the society's area code whether society's area code at its place calculate with last iteration is identical, if so, execution step (6), otherwise, execution step 5b);
(6) obtain the community network node in each community:
Very big factions with in each community of all community network node replacements in very big factions, obtain the community network node in each community.
Compared with prior art, tool has the following advantages in the present invention:
First, during the community network node of the present invention in obtaining each community, first from community network, find out very big factions, then find out the community at each very big factions place, with the very big factions in each community of all community network node replacements in very big factions, overcome prior art and cannot find the deficiency of overlapping community, made the present invention there is the ability of finding overlapping community.
Second, the present invention is when calculating community's Attraction Degree, by changing the size of multi-scale parameters, obtain different community's Attraction Degree, thereby obtain the community structure under different levels, overcome the shortcoming that prior art can not obtain the community structure under different levels, made the present invention to there is the ability that can obtain the community structure under different levels.
The 3rd, the present invention is when calculating random movement probability, first from community network, find out very big factions, then calculate the random movement probability of very big factions to community, find out the community at each very big factions place, thereby obtain the community network node in each community, overcome the shortcoming of community's unstable result that prior art obtains, make the present invention to have improved the stability of community discovery result.
Accompanying drawing explanation
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is the process flow diagram that step 5 of the present invention is found out the community at each very big factions place;
Fig. 3 is analogous diagram of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the present invention is described in further detail.
With reference to Fig. 1, the concrete steps that the present invention realizes are as follows:
Step 1 is found out very big factions from community network.
The 1st step, an optional node v in community network, is assigned to set Y by the neighbor node set of node v, and node v joins in set X;
The 2nd step, in pair set Y, the label of node is done ascending sort according to order from small to large;
The 3rd step, in the node of set Y, elects the node of smallest sequence number as node t, and node t is joined in set X;
The 4th step, whether the node in judgement set X in the neighbor node set of each node in community network, if so, the node in community network is joined can with set X in node form in the node set of factions, otherwise, do not add;
The 5th step, whether judgement can be empty set with the node set of gathering the node formation factions in X, if so, carries out the 7th step, otherwise carries out the 6th step;
The 6th step, joins set X by node t, can again be assigned to set Y with the node set of gathering the node formation factions in X, carries out the 2nd step;
The 7th step, whether the node in judgement set X is included in any one other factions, if so, do not export, otherwise the node in set X forms very big factions, the node in output set X;
The 8th step, whether the node in judgement set Y is all processed complete, if so, carries out the 9th step, otherwise carries out the 3rd step;
The 9th step, judges that whether the node in community network is all processed complete, if so, performs step (2), otherwise carries out the 1st step.
Step 2, processes unnecessary very big factions and isolated node.
2a) optional very big factions in found out very big factions;
The node sum and the node in selected very big factions that 2b) compare in each very big factions are total, find out the very big factions that are greater than the node sum in selected very big factions;
2c) adopt degree of comprising value formula, calculate degree of the comprising value of the very big factions more than the node sum in selected very big factions with respect to node sum of selected very big factions, degree of comprising value formula is as follows:
Wherein, C (i, j) represents that the very big j of factions is with respect to the degree of comprising of the very big i of factions, V irepresent the node set comprising in the very big i of factions, V jrepresent the node set comprising in the very big j of factions, ∩ represents V iand V jdo intersection operation.
2d) in judgement degree of comprising value, whether be greater than 0.75, if so, from found out very big factions set, delete selected very big factions, otherwise, retain selected very big factions, execution step 2e);
2e) judge that whether the very big factions in community network are all processed complete, if so, perform step 2f), otherwise, execution step 2a);
2f) travel through all very big factions, find out the isolated node not being included in any one very big factions;
2 g) isolated node is joined in the very big factions that the neighbor node number that comprises isolated node is maximum;
Step 3, constructs very big factions network.
3a) optional two very big factions in very big factions, adopt degree of overlapping formula, calculate the degree of overlapping of selected two very big factions, and degree of overlapping formula is as follows:
δ ( d , c ) = | V d ∩ V c | min ( | V d | , | V c | )
Wherein, δ (d, c) represents the degree of overlapping of the very big d of factions and the very big c of factions, V drepresent the node set comprising in the very big d of factions, V crepresent the node set comprising in the very big c of factions, ∩ represents V dand V cdo intersection operation, min is illustrated in | V d| and | V c| in get minimum value operation.
Whether the degree of overlapping that 3b) judges every two very big factions has all been calculated, and if so, performs step 3c), otherwise, execution step 3a);
3c) degree of overlapping is greater than between two very big factions of 0.2 and sets up a limit, form very big factions network;
Step 4, initialization tight ness rating matrix.
4a) optional two very big factions in very big factions, adopt tight ness rating formula, calculate the tight ness rating of selected two very big factions, and tight ness rating formula is as follows:
m pq=1+|Γ p∩Γ q|
Wherein, m pqthe tight ness rating value that represents the very big p of factions and the very big q of factions, Γ prepresent the very big factions of the neighbours set of the very big p of factions, Γ qrepresent the very big factions of the neighbours set of the very big q of factions, ∩ represents Γ pand Γ qdo intersection operation.
Whether the tight ness rating that 4b) judges every two very big factions has all been calculated, if so, perform step (5), otherwise, execution step 4a);
Step 5, finds out the community at each very big factions place.
5a) each very big factions is constructed respectively to an initial community for correspondence with it, in each initial community, only have very big factions;
5b) optional very big factions in very big factions, obtain community's set at the very big factions of the neighbours place of selected very big factions;
5c) calculate the community Attraction Degree of each community to selected very big factions in the set of community, neighbours very big factions place, community's Attraction Degree formula is as follows:
A ( a , k ) = [ Σ s ∈ Γ ∩ R k m as Σ f , e ∈ Γ a ∩ R k m fe Σ b , w ∈ R k m bw ] t
Wherein, A (a, k) represents the community Attraction Degree of k community to the very big a of factions, and s is illustrated in the very big factions of neighbours of the very big a of factions in k community, Γ arepresent the very big factions of the neighbours set of the very big a of factions, R krepresent k community, ∩ represents Γ aand R kdo intersection operation, m asthe tight ness rating value that represents the very big a of factions and the very big s of factions, ∑ represents all R kthe very big factions of neighbours of the very big a of factions in community and the greatly tight ness rating of a of factions are carried out sum operation, and f and e represent two the very big factions of different neighbours of the very big a of factions in k community, m fethe tight ness rating that represents the very big f of factions and the very big e of factions, ∑ represents all R kthe tight ness rating summation of every two the very big factions of neighbours of the very big a of factions in community, b and w represent the very big factions that two in k community are different, m bwthe tight ness rating that represents the very big b of factions and the very big w of factions, ∑ represents R kthe tight ness rating sum operation of every two the very big factions in community, t represents multi-scale parameters, by changing the size of t, can obtain the community structure under different levels.
5d) calculate the random movement probability of selected very big factions to each community in the set of community, neighbours very big factions place, obtain largest random movement probability, random movement probability formula is as follows:
X ( a , k ) = A ( a , k ) Σ R h ∈ R a ′ A ( a , h )
Wherein, X (a, k) represents the random movement probability of the very big a of factions to k community, and A (a, k) represents the community Attraction Degree of k community to the very big a of factions, R hthe community that represents the very big factions of the neighbours place of the very big a of factions, R' arepresent community's set at the very big factions of the neighbours place of the very big a of factions, A (a, h) represent the community Attraction Degree of h community to the very big a of factions, ∑ represents the community's Attraction Degree sum operation to the very big a of factions to each community in community's set at the very big factions of the neighbours of the very big a of factions place.
5e) the community from own place by selected very big factions, the community corresponding to largest random movement probability moves, and obtains society's area code at selected very big factions place in current iteration;
5f) all very big factions are judged whether to obtain society's area code at its place, if so, perform step 5g), otherwise, execution step 5b);
5g) to all very big factions, judge that the society's area code whether society's area code at its place calculate with last iteration is identical, if so, execution step (6), otherwise, execution step 5b);
Step 6, obtains the community network node in each community.
Very big factions with in each community of all community network node replacements in very big factions, obtain the community network node in each community.
Effect of the present invention can be further described by following emulation experiment.
1, simulated conditions:
Emulation of the present invention is under Intel (R) Xeon (R) CPU, the hardware environment of 4G internal memory and the development environment of Eclipse 3.2, realizes that program carries out with Java language.Emulation experiment is used data from true community network Zachary ' s Karate club network, node in club's network represents clubbite, social interaction between the line-up of delegates of limit, Zachary ' s Karate club network includes 34 members and 78 limits altogether.
2, emulation content:
In conjunction with the community discovery method based on factions' random walk of the present invention, Zachary ' s Karate club network is carried out to community discovery, finally obtain the community network node in each community.
3. analysis of simulation result:
Fig. 3 is the analogous diagram to Zachary ' s Karate club network.Numbering in Fig. 3 in circle represents node, and wherein, node 1,2,3,4,5,6,7,8,9,10,11,12,13,14,17,18,20,22 belongs to community 1. Node 3,9,15,16,19,21,23,24,25,26,27,28,29,30,31,32,33,34 belongs to community 2, wherein node 3 and node 9 are overlapping nodes of community 1 and community 2, and the present invention can obtain the community discovery result of network as can be seen here.

Claims (7)

1.基于派系随机游走的社区发现方法，包括如下步骤：1. A community discovery method based on faction random walk, including the following steps: （1）从社会网络中找出极大派系：(1) Find the largest faction from the social network: （2）处理多余的极大派系和孤立节点：(2) Handle redundant maximal factions and isolated nodes: 2a）在所找出的极大派系中任选一个极大派系；2a) Choose a maximal faction among the found maximal factions; 2b）比较每一个极大派系中的节点总数和所选极大派系中的节点总数，找出大于所选极大派系中的节点总数的极大派系；2b) Compare the total number of nodes in each maximal faction with the total number of nodes in the selected maximal faction, and find the maximal faction that is greater than the total number of nodes in the selected maximal faction; 2c）采用包含度值公式，计算所选极大派系相对于节点总数比所选极大派系中的节点总数多的极大派系的包含度值；2c) Using the inclusion degree formula, calculate the inclusion degree value of the selected maximal faction relative to the maximal faction whose total number of nodes is more than the total number of nodes in the selected maximal faction; 2d）判断包含度值中是否大于0.75，若是，则从所找出的极大派系集合中删除所选极大派系，否则，保留所选极大派系，执行步骤2e）；2d) Determine whether the inclusion degree is greater than 0.75, if so, delete the selected maximum faction from the found maximum faction set, otherwise, keep the selected maximum faction, and perform step 2e); 2e）判断社会网络中的极大派系是否都被处理完，若是，则执行步骤2f），否则，执行步骤2a）；2e) Determine whether all the largest factions in the social network have been dealt with, if so, perform step 2f), otherwise, perform step 2a); 2f）遍历所有的极大派系，找出不包含在任何一个极大派系中的孤立节点；2f) Traverse all maximal factions and find out the isolated nodes that are not included in any maximal faction; 2g）将孤立节点加入到包含孤立节点的邻居节点数最多的极大派系中；2g) Join the orphan node to the maximal faction with the largest number of neighbor nodes containing the orphan node; （3）构造极大派系网络：(3) Construct a very large faction network: 3a）在极大派系中任选两个极大派系，采用重叠度公式，计算所选的两个极大派系的重叠度；3a) Choose two maximal factions among the maximal factions, and use the overlap degree formula to calculate the overlap degree of the selected two maximal factions; 3b）判断每两个极大派系的重叠度是否都计算完，若是，则执行步骤3c），否则，执行步骤3a）；3b) Determine whether the overlapping degree of each two maximum factions has been calculated, if so, perform step 3c), otherwise, perform step 3a); 3c）将重叠度大于0.2的两个极大派系之间建立一条边，构成极大派系网络；3c) Establish an edge between two maximal factions with an overlap greater than 0.2 to form a maximal faction network; （4）初始化紧密度矩阵：(4) Initialize the compactness matrix: 4a）在极大派系中任选两个极大派系，采用紧密度公式，计算所选的两个极大派系的紧密度；4a) Select two maximal factions among the maximal factions, and use the compactness formula to calculate the compactness of the two selected maximal factions; 4b）判断每两个极大派系的紧密度是否都计算完，若是，则执行步骤（5），否则，执行步骤4a）；4b) Determine whether the closeness of each two maximal factions has been calculated, if so, perform step (5), otherwise, perform step 4a); （5）找出每个极大派系所在的社区：(5) Find out which community each maximal faction is in: 5a）对每个极大派系分别构造一个与之对应的初始社区,每个初始社区中只有一个极大派系；5a) Construct a corresponding initial community for each maximal faction, and there is only one maximal faction in each initial community; 5b）在极大派系中任选一个极大派系，得到所选极大派系的邻居极大派系所在的社区集合；5b) Choose a maximal faction among the maximal factions, and get the community set where the neighbor maximal factions of the selected maximal faction are located; 5c）计算邻居极大派系所在社区集合中每个社区对所选极大派系的社区吸引度；5c) Calculate the community attraction of each community in the set of communities where the neighbor maximum faction is located to the selected maximum faction; 5d）计算所选极大派系对邻居极大派系所在社区集合中每个社区的随机移动概率，得到最大随机移动概率；5d) Calculate the random movement probability of the selected maximum faction to each community in the community set where the neighbor maximum faction is located, and obtain the maximum random movement probability; 5e）将所选极大派系从自己所在的社区，向最大随机移动概率对应的社区移动，得到在当前迭代中所选极大派系所在的社区号；5e) Move the selected extreme faction from the community where it is located to the community corresponding to the maximum random movement probability, and obtain the community number of the selected extreme faction in the current iteration; 5f）对所有的极大派系判断是否得到其所在的社区号，若是，执行步骤5g），否则，执行步骤5b）；5f) For all extremely large factions, judge whether the community number they belong to is obtained, if so, perform step 5g), otherwise, perform step 5b); 5g）对所有的极大派系，判断其所在的社区号是否与上次迭代计算得到的社区号相同，若是，则执行步骤（6），否则，执行步骤5b）；5g) For all extremely large factions, judge whether the community number they are in is the same as the community number calculated in the last iteration, if so, perform step (6), otherwise, perform step 5b); （6）得到每个社区中的社会网络节点：(6) Get the social network nodes in each community: 用极大派系中的所有社会网络节点替换每个社区中的极大派系，得到每个社区中的社会网络节点。Replace the max faction in each community with all the social network nodes in the max clique to get the social network nodes in each community. 2.根据权利要求1所述的基于派系随机游走的社区发现方法,其特征在于,步骤（1）中所述的从社会网络中找出极大派系的具体步骤如下：2. The community discovery method based on faction random walk according to claim 1, characterized in that, the specific steps of finding the largest faction from the social network described in step (1) are as follows: 第1步，在社会网络中任选一个节点v，将节点v的邻居节点集合赋给集合Y，节点v加入到集合X中；Step 1, select a node v in the social network, assign the set of neighbor nodes of node v to set Y, and add node v to set X; 第2步，对集合Y中节点的标号按照从小到大的顺序做升序排序；Step 2, sort the labels of the nodes in the set Y in ascending order from small to large; 第3步，在集合Y的节点中，将最小序号的节点选为节点t，将节点t加入到集合X中；Step 3: Among the nodes of set Y, select the node with the smallest serial number as node t, and add node t to set X; 第4步，判断集合X中的节点是否在社会网络中的每个节点的邻居节点集合内，若是，则将社会网络中的节点加入到能与集合X中的节点构成派系的节点集合中，否则，不加入；Step 4, determine whether the nodes in the set X are in the set of neighbor nodes of each node in the social network, if so, add the nodes in the social network to the set of nodes that can form factions with the nodes in the set X, Otherwise, do not join; 第5步，判断能与集合X中的节点构成派系的节点集合是否为空集，若是，则执行第7步，否则执行第6步；Step 5, judge whether the node set that can form a faction with the nodes in the set X is an empty set, if so, execute step 7, otherwise execute step 6; 第6步，将节点t加入到集合X,将能与集合X中的节点构成派系的节点集合重新赋给集合Y，执行第2步；Step 6: Add node t to set X, reassign the set of nodes that can form a faction with the nodes in set X to set Y, and execute step 2; 第7步，判断集合X中的节点是否包含在任何一个其他的派系中，若是，则不输出,否则，集合X中的节点组成一个极大派系，输出集合X中的节点；Step 7, judge whether the nodes in the set X are included in any other faction, if so, do not output, otherwise, the nodes in the set X form a maximum faction, and output the nodes in the set X; 第8步，判断集合Y中的节点是否都被处理完，若是，则执行第9步，否则执行第3步；Step 8, judge whether all the nodes in the set Y have been processed, if so, execute step 9, otherwise execute step 3; 第9步，判断社会网络中的节点是否都被处理完，若是，则执行步骤(2)，否则执行第1步。Step 9, judge whether all the nodes in the social network have been processed, if so, execute step (2), otherwise execute step 1. 3.根据权利要求1所述的基于派系随机游走的社区发现方法，其特征在于，步骤2c）中所述的包含度值公式如下:3. The community discovery method based on faction random walk according to claim 1, characterized in that the inclusion degree formula described in step 2c) is as follows: CC (( ii ,, jj )) == || VV ii ∩∩ VV jj || || VV ii || 其中，C(i,j)表示极大派系j相对于极大派系i的包含度，Vi表示极大派系i中包含的节点集合，Vj表示极大派系j中包含的节点集合，∩表示对Vi和Vj做交集操作。Among them, C(i, j) represents the inclusion degree of maximal faction j relative to maximal faction i, V i represents the node set contained in maximal faction i, V j represents the node set contained in maximal faction j, ∩ Indicates the intersection operation on V i and V j . 4.根据权利要求1所述的基于派系随机游走的社区发现方法，其特征在于，步骤3a）中所述的重叠度公式如下：4. The community discovery method based on faction random walk according to claim 1, characterized in that the formula of overlap degree in step 3a) is as follows: δδ (( dd ,, cc )) == || VV dd ∩∩ VV cc || minmin (( || VV dd || ,, || VV cc || )) 其中，δ(d,c)表示极大派系d和极大派系c的重叠度，Vd表示极大派系d中包含的节点集合，Vc表示极大派系c中包含的节点集合，∩表示对Vd和Vc做交集操作，min表示在|Vd|和|Vc|中取最小值操作。Among them, δ(d, c) represents the overlapping degree of the maximum faction d and the maximum faction c, V d represents the node set contained in the maximum faction d, V c represents the node set contained in the maximum faction c, ∩ represents Perform the intersection operation on V d and V c , and min means to take the minimum value operation between |V d | and |V c |. 5.根据权利要求1所述的基于派系随机游走的社区发现方法，其特征在于，步骤4a）中所述的紧密度公式如下：5. The community discovery method based on faction random walk according to claim 1, characterized in that the compactness formula described in step 4a) is as follows: mpq=1+|Γp∩Γq|m pq =1+|Γ p ∩Γ q | 其中，mpq表示极大派系p和极大派系q的紧密度值，Γp表示极大派系p的邻居极大派系集合，Γq表示极大派系q的邻居极大派系集合，∩表示对Γp和Γq做交集操作。Among them, m pq represents the closeness value of the maximum faction p and the maximum faction q, Γ p represents the maximum faction set of neighbors of the maximum faction p, Γ q represents the maximum faction set of neighbors of the maximum faction q, and ∩ represents the Γ p and Γ q do the intersection operation. 6.根据权利要求1所述的基于派系随机游走的社区发现方法，其特征在于，步骤5c）中所述的社区吸引度按照下式进行计算：6. The community discovery method based on faction random walk according to claim 1, characterized in that the community attractiveness described in step 5c) is calculated according to the following formula: AA (( aa ,, kk )) == [[ ΣΣ sthe s ∈∈ ΓΓ ∩∩ RR kk mm asas ΣΣ ff ,, ee ∈∈ ΓΓ aa ∩∩ RR kk mm fefe ΣΣ bb ,, ww ∈∈ RR kk mm bwbw ]] tt 其中，A(a,k)表示第k个社区对极大派系a的社区吸引度，s表示在第k个社区中的极大派系a的邻居极大派系，Γa表示极大派系a的邻居极大派系集合，Rk表示第k个社区，∩表示对Γa和Rk做交集操作，mas表示极大派系a和极大派系s的紧密度值，∑表示对所有Rk社区中的极大派系a的邻居极大派系和极大派系a的紧密度进行求和操作，f和e表示第k个社区中的极大派系a的两个不同的邻居极大派系，mfe表示极大派系f和极大派系e的紧密度，∑表示对所有Rk社区中的极大派系a的每两个邻居极大派系的紧密度求和，b和w表示第k个社区中的两个不同的极大派系，mbw表示极大派系b和极大派系w的紧密度，∑表示对Rk社区中的每两个极大派系的紧密度求和操作，t表示多尺度参数,通过改变t的大小，可得到不同层次下的社区结构。Among them, A(a,k) represents the community attraction of the kth community to the maximum faction a, s represents the neighbor maximum faction of the maximum faction a in the kth community, Γ a represents the maximum faction a Neighboring maximum faction set, R k represents the kth community, ∩ represents the intersection operation on Γ a and R k , ma as represents the closeness value of the maximum faction a and the maximum faction s, ∑ represents the value of all R k communities The maximal faction of the neighbor maximal faction of the maximal faction a in and the closeness of the maximal faction a are summed, f and e represent two different maximal factions of the maximal faction a in the kth community, m fe Indicates the closeness of the maximum faction f and the maximum faction e, ∑ represents the summation of the closeness of every two neighboring maximum factions of the maximum faction a in all R k communities, b and w represent the kth community Two different maximal cliques of , m bw denotes the closeness of maximal clique b and maximal clique w, ∑ denotes the summation operation of the closeness of every two maximal cliques in the R k community, t denotes multi-scale parameter, by changing the size of t, the community structure at different levels can be obtained. 7.根据权利要求1所述的基于派系随机游走的社区发现方法，其特征在于，步骤5d）中所述的随机移动概率按照下式计算：7. The community discovery method based on faction random walk according to claim 1, characterized in that the random movement probability described in step 5d) is calculated according to the following formula: Xx (( aa ,, kk )) == AA (( aa ,, kk )) ΣΣ RR hh ∈∈ RR aa ′′ AA (( aa ,, hh )) 其中，X(a,k)表示极大派系a对第k个社区的随机移动概率，A(a,k)表示第k个社区对极大派系a的社区吸引度，Rh表示极大派系a的邻居极大派系所在的社区，R'a表示极大派系a的邻居极大派系所在的社区集合，A(a,h)表示第h个社区对极大派系a的社区吸引度,∑表示对极大派系a的邻居极大派系所在的社区集合中的每个社区对极大派系a的社区吸引度求和操作。Among them, X(a,k) represents the random movement probability of the maximum faction a to the kth community, A(a,k) represents the community attraction of the kth community to the maximum faction a, R h represents the maximum faction The community where the maximum faction of the neighbor of a is located, R' a represents the set of communities where the maximum faction of the maximum faction a is located, A(a,h) represents the community attraction of the hth community to the maximum faction a, ∑ Indicates the summation operation of the community attraction of each community in the community set where the maximum faction a's neighbors are located to the maximum faction a.
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