CN103020267B - Based on the complex network community structure method for digging of triangular cluster multi-label - Google Patents

Abstract

Based on a complex network community mining method for triangular cluster multi-label, comprise the following steps: mutually disjoint triangular cluster in search network; For the initial state that the mutually different label of the Node configuration in different triangular cluster is propagated as label; According to many tag update rules, for all nodes in network, the propagation synchronously carrying out label upgrades; By the label array that obtains after upgrading with upgrade the label array obtained before and compare; If label is still in propagation, then proceed to upgrade; If label produces vibration, then proceed again after carrying out vibration Processing for removing to upgrade; If label no longer changes, then stop upgrading, obtain the community structure with overlap in network.Time complexity of the present invention is very low, is applicable to large-scale complex network.In addition, the present invention can detect the lap of community structure well, and has good robustness, and the accuracy of detection is very high.

Description

Based on the complex network community structure method for digging of triangular cluster multi-label

Technical field

What the present invention relates to is a kind of method of complex network field, specifically a kind of complex network community structure method for digging based on triangular cluster multi-label.

Background technology

Complex network is a kind of abstract representa-tions of complication system in real world, individuality in node on behalf complication system in complex network, a kind of relation of the connection between node then according to certain regular self-assembling formation or arteface between individuality in representative system.At present, complex network has been widely used in characterizing the various complication systems such as electric power networks, communication network, internet, social networks.

Community structure is the important topological property of of complex network, and whole complex network is made up of several community structures, and the node of each community structure inside connects closely, and the connection between community structure is then relatively sparse.The community structure of complex network corresponds to the functional unit or the organizations that have common feature in reality, such as in internet, community structure is exactly that the number of site of topics common is discussed, and the community structure in social networks is exactly a group of the people's composition having common interest hobby.Therefore, the characteristic of network is analyzed by the community structure excavated in complex network and function is of great practical significance.

The community structure of complex network excavates the crucial character of demand fulfillment two:

The first, complexity is low.The scale of complex network is often very huge, and can comprise several thousand even up to ten thousand nodes, under the network of this scale, if the complexity of method is higher, the time overhead so carrying out community structure excavation will be very large;

The second, effective overlay structure testing mechanism.In actual complex network, community structure ubiquity overlapping phenomenon, some nodes namely in complex network can belong to multiple community structure simultaneously, and this just requires that community structure method for digging can detect the lap of community structure in complex network.

Find by literature search, M.E.J.Newman and M.Girvan proposes a kind of community mining method based on shortest path in article " Communitystructureinsocialandbiologicalnetworks [J] " (" community structure in social activity and bio-networks ") (Proc.Natl.Acad.Sci.USA99,7821-7826 (2001)) (PNAS).First the method by the shortest path between any two points in computational grid, obtains the shortest path table of whole network; Then the number of times utilizing this table to add up to be passed through by shortest path on every bar limit as the weights on this limit, and removes the limit of maximum weight in network, recalculates the weights on each bar limit in whole network afterwards; Repeat above step, until whole network is divided into rational community structure.The accuracy of detection of the program is not high, and method complexity is higher, and cannot detect the community structure with overlap.

Find through retrieval again, the people such as FilippoRadicchi and ClaudioCastellano propose a kind of community mining scheme based on Local network topology structure at article " Definingandidentifyingcommunitiesinnetworks [J] " (" definition community structure " in recognition network) in (Proc.Natl.Acad.Sci.USA101,2658-2663 (2004)) (PNAS).Its method is: the first local topology feature of community structure in Analysis of Complex network, and using the triangular structure in network as the most basic structure of Web Community, and in statistics network, the quantity of the triangular structure of every bar limit institute subordinate is as the weights on this limit; Then, remove the limit of maximum weight in network, recalculate the weights on each bar limit in whole network; Repeat above step, until whole network is divided into rational community structure.The program take into account the local features of network topology structure, and accuracy of detection has a certain upgrade, but still cannot solve this two problems of detection of complexity height and community structure lap.

Find through retrieval again, the people such as GergelyPalla and ImreDerenyi propose a community structure method for digging based on complete subgraph in article " Uncoveringtheoverlappingcommunitystructureofcomplexnetwo rksinnatureandsociety [J] " (" excavate in nature and community network and have overlapping community structure ") (Nature435 (7043), 814-818 (2005)) (nature).For each node in complex network, first calculate all complete subgraphs comprising this node, construct the overlapping matrix of these complete subgraphs; Then filter according to connectivity pair overlapping matrix, thus obtain that there is overlapping community structure.Although the method can be excavated have overlapping community structure, because complexity is too high, not there is actual using value.

Find finally by retrieval, the people such as U.N.Raghavan and R.Albert propose a kind of label transmission method being applied to community structure and excavating in article " Nearlineartimealgorithmtodetectcommunitystructuresinlarg e-scalenetworks [J] " (being applied to a kind of method close to linear time complexity that in large scale network, community structure is excavated) (Phys.Rev.E76,036106 (2007)) (physical comment).First each peer distribution one the independently label in complex network is given during program initialization; Be all in its neighbor node, occupy the maximum label of ratio afterwards by the tag update of each node when each iteration, until stop iteration when the label of all nodes all no longer changes in network, the node now having same label just belongs to same community structure.Thus, the community structure of complex network can just be marked off.The method complexity is very low, has close to linear time complexity, goes for large-scale complex network.But the robustness of the method is very poor, accuracy of detection is not high, and cannot detect the community structure with overlap.

Summary of the invention

The object of the invention is to for above-mentioned the deficiencies in the prior art, propose a complex network community structure method for digging based on triangular cluster multi-label.Its main thought is the initial state that the core first finding community structure is propagated as label, adopts many tag updates rule afterwards, ensure the Detection results of community structure lap in the renewal of label.

The present invention is achieved through the following technical solutions:

Based on a complex network community mining method for triangular cluster multi-label, its feature is: the method comprises the following steps: mutually disjoint triangular cluster in search network; For the initial state that the mutually different label of the Node configuration in different triangular cluster is propagated as label; According to many tag update rules, for all nodes in network, the propagation synchronously carrying out label upgrades; By the label array that obtains after upgrading with upgrade the label array obtained before and compare; If label is still in propagation, then proceed to upgrade; If label produces vibration, then proceed again after carrying out vibration Processing for removing to upgrade; If label no longer changes, then stop upgrading, obtain the community structure with overlap in network.

The concrete steps of the method are as follows:

1. for each node of complex network G to be measured gives an empty label;

2. by following formulae discovery every bar limit e _ijtriangular cluster coefficient T C (e _ij):

TC(e _ij)＝|N(v _i)∩N(v _j)|

Wherein: N (v _i) be node v _ithe set of neighbor node, ∩ is the operational symbol sought common ground, || be the operational symbol asking cardinal of the set, i be 1,2,3 ..., N;

3. the limit that triangular cluster coefficient is maximum is searched out;

4. all nodes in the triangular cluster on this limit being given a radix being different from other labels in network is the label of 1; Afterwards these nodes are deleted from network, obtain new network G ',

5. judge whether to exist the limit that triangular cluster coefficient is greater than 0, exist, then return step 2., otherwise the label of all nodes in now network is saved as a label array L ⁽⁰⁾, as the original state that label is propagated, enter step 6.;

6. the propagation utilizing following formula synchronously to carry out label upgrades:

$L_i^{\left(t\right)}=\arg \underset{l}{\max }\underset{v_j\∈N\left(v_i\right)}{\mathrm{\Σ}}\mathrm{\δ}(L_j^{(t-1)},l)$

$\mathrm{\δ}(L_j^{(t-1)},l)=\left\{\begin{array}{cc}1,& l\∈L_j^{(t-1)}\\ 0,& l\∉L_j^{(t-1)}\end{array}\right.$

Wherein: node v _icarry out the label after upgrading for the t time, t is the positive integer of more than 1, N (v _i) be node v _ithe set of neighbor node, node v _ineighbor node v _jlabel after upgrading at the t-1 time, be the operational symbol of the set asking element l, the function that the l tried to achieve defines after making max obtains maximal value.When upgrading for the t time, utilizing and upgrading the label array L obtained the t-1 time ^(t-1), for the rule of all nodes in complex network G according to many tag updates, the propagation synchronously carrying out label upgrades, and is saved to new label array L ^(t);

7. label array is compared: upgrade the t time the label array L obtained ^(t)with upgrade the label array L obtained before for t-1 time ⁽¹⁾, L ⁽²⁾..., L ^(t-1)compare,

When the label array of t time is all not identical, then return step 6.;

Work as L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)middle existence and L ^(t)identical label array, then enter and show that vibration has appearred in renewal, then carry out step 8.;

As label array L ^(t-1)and L ^(t)identical, then enter step 9.

8. vibrate Processing for removing: assuming that label array L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)in there is L ^(k)and L ^(t)identical, then at label array L ^(k+1)..., L ^(t)in search out all from kth be updated to for+1 time the t time upgrade label occurred change node, at L ^(t)it is middle that the label of these nodes to be replaced to respectively the radix being different from other labels in network be the label of 1; Then step is returned 6.;

What 9. obtain network has overlapping community structure, and the node having same label element in network belongs to same community structure, and the node that label radix is greater than 1 is the lap of community structure.

Technical solution of the present invention is explained as follows:

1. calculate the original state that label is propagated:

For complex network G=(V, E) to be measured, wherein V={v _i| i=1,2 ..., N} is the node set of complex network G, v _irepresent i-th node, N is the quantity of Node Contraction in Complex Networks, the limit set of complex network G, e _ij=(v _i, v _j) represent connected node v in network _iand v _jlimit, be each node v in network G _i(i=1,2 ..., N) give an empty label.First, every bar limit e is calculated _ij(i, j=1,2 ..., N) triangular cluster coefficient; Then, search out the limit that triangular cluster coefficient is maximum, all nodes in the triangular cluster on this limit being reset a radix being different from other labels in network is the label of 1; Afterwards these nodes are deleted from network, obtain new network G '=(V', E ');

Repeat said process, until there is not the limit that triangular cluster coefficient is greater than 0 in network, the label of all nodes in now network is saved as a label array as the original state that label is propagated, wherein represent the label of node vi when original state propagated by label;

2. the propagation of label upgrades:

When upgrading for the t time, utilizing and upgrading the label array L obtained the t-1 time ^(t-1), for the rule of all nodes in complex network G=(V, E) according to many tag updates, the propagation synchronously carrying out label upgrades, and is saved to new label array $L^{\left(t\right)}=[L_1^t,L_2^t,...,L_i^t,...,L_N^t],$ Wherein represent node v _ilabel after upgrading at the t time;

3, label array compares:

The label array L obtained is upgraded by the t time ^(t)with upgrade the label array L obtained before for t-1 time ⁽¹⁾, L ⁽²⁾..., L ^(t-1)compare,

When the label array of t time is all not identical, then the propagation continuing to carry out according to step 2 label upgrades;

Work as L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)middle existence and L ^(t)identical label array, then show that vibration has appearred in renewal, must carry out vibration Processing for removing, and the propagation continuing to carry out according to step 2 label afterwards again upgrades;

As label array L ^(t-1)and L ^(t)identical, then show network G=(V, E) in, the label of all nodes all no longer changes, the propagation now stopping label upgrades, namely the node having same label element in network belongs to same community structure, and the node that label radix is greater than 1 is the lap of community structure.

The original state that described calculating label is propagated.For complex network G=(V, E) to be measured, wherein V={v _i| i=1,2 ..., N is the node set of complex network G, and vi represents i-th node, and N is the quantity of Node Contraction in Complex Networks, E={e _ij=(v _i, v _j) | i, j=1,2 ..., N} is the limit set of complex network G, e _ij=(v _i, v _j) represent connected node v in network _iand v _jlimit, be each node v in network G _i(i=1,2 ... N, gives an empty label.First, every bar limit e is calculated _ij(i, j=1,2 ..., N) triangular cluster coefficient; Then, search out the limit that triangular cluster coefficient is maximum, all nodes in the triangular cluster on this limit being reset a radix being different from other labels in network is the label of 1; Afterwards these nodes are deleted from network, obtain new network G '=(V', E').Repeat said process, until there is not the limit that triangular cluster coefficient is greater than 0 in network.The label of all nodes in now network is saved as a label array as the original state that label is propagated, wherein represent node v _ilabel when original state propagated by label.Be specially:

Described limit e _ijtriangular cluster, refer in network and comprise limit e _ijthe topological structure of all triangles composition.

Described limit e _ijtriangular cluster coefficient, refer in network and comprise limit e _ijall leg-of-mutton quantity, its computing formula is as follows:

TC(e _ij)＝|N(v _i)∩N(v _j)|

Wherein, TC (e _ij) be limit e _ijtriangular cluster coefficient, N (v _i) be node v _ithe set of neighbor node, ∩ is the operational symbol sought common ground, || be the operational symbol asking cardinal of the set.

Described node v _ineighbor node, to refer in network and node v _ibetween have the node of fillet.

Described cardinality of a set, refers to the number of element in set.

Described node v _ilabel, be one set L _i={ l _ik| k=1,2 ..., K}, its element l _ikbe used for characterizing node v _ithe numbering of affiliated community structure, K is cardinality of a set.If the radix of this label is 1, then show node v _ionly belong to a community structure; If the radix of this label is greater than 1, then node v _ibelong to multiple community structure simultaneously.

Described empty label, refer to the label of set for empty set, namely radix is the label of 0.The label that node has is empty label, then illustrate that this node does not belong to any community structure.

Described label array is the array of a 1 × N, for preserving the label of all nodes in network.Wherein, N is the quantity of nodes, represent the label that all nodes have when original state propagated by label, for node v during label propagation original state _ithe label had; represent the label that after upgrading for the t time, all nodes have, be upgrade posterior nodal point v the t time _ithe label had.

The propagation of described label upgrades.When upgrading for the t time, utilizing and upgrading the label array L obtained the t-1 time ^(t-1), for the rule of all nodes in complex network G=(V, E) according to many tag updates, the propagation synchronously carrying out label upgrades, and is saved to new label array wherein represent node v _ilabel after upgrading at the t time.Be specially:

Described many tag updates rule is:

$L_i^{\left(t\right)}=\arg \underset{l}{\max }\underset{v_j\∈N\left(v_i\right)}{\mathrm{\Σ}}\mathrm{\δ}(L_j^{(t-1)},l)$

$\mathrm{\δ}(L_j^{(t-1)},l)=\left\{\begin{array}{cc}1,& l\∈L_j^{(t-1)}\\ 0,& l\∉L_j^{(t-1)}\end{array}\right.$

Wherein, node v _icarry out the label after upgrading for the t time, t is the positive integer of more than 1, N (v _i) be node v _ithe set of neighbor node, node v _ineighbor node v _jlabel after upgrading at the t-1 time, be the operational symbol of the set asking element l, the function that the l tried to achieve defines after making max obtains maximal value.

The described propagation synchronously carrying out label upgrades, and refers to and upgrades arbitrary node v the t time _ilabel can only by upgrading the label array L obtained t-1 time before ⁽¹⁾, L ⁽²⁾..., L ^(t-1)calculate, and other any node v obtained with the t time renewal _jthe label of (j ≠ i) irrelevant.

Described label array compares.The label array L obtained is upgraded by the t time ^(t)with upgrade the label array L obtained before for t-1 time ⁽¹⁾, L ⁽²⁾..., L ^(t-1)compare.If the label array of t time is all not identical, then the propagation continuing to carry out according to step 2 label upgrades; If L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)middle existence and L ^(t)identical label array, then show that vibration has appearred in renewal, must carry out vibration Processing for removing, and the propagation continuing to carry out according to step 2 label afterwards again upgrades; If label array L ^(t-1)and L ^(t)identical, then show network G=(V, E) in, the label of all nodes all no longer changes, the propagation now stopping label upgrades, namely the node having same label element in network belongs to same community structure, and the node that label radix is greater than 1 is the lap of community structure.Be specially:

Described vibration is eliminated, and the steps include: supposition label array L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)in there is L ^(k)and L ^(t)identical, then at label array L ^(k+1)..., L ^(t)in search out all from kth be updated to for+1 time the t time upgrade label occurred change node, at L ^(t)it is middle that the label of these nodes to be replaced to respectively the radix being different from other labels in network be the label of 1.

The present invention improves performance and the effect of label propagation from three aspects.First, the core texture of complex network community structure is triangular cluster.The present invention marks off disjoint triangular cluster from network, and distribute the initial state that different labels is propagated as label, take full advantage of the topological property of complex network, the Primary Construction basic configuration of community structure, being in a ratio of the mutually different label of all peer distribution in network has had very large optimization as the method for initial state.Secondly, invention introduces many tag updates rule, the label of each node is made to propagate the label information upgrading and take full advantage of neighbor node, the local message of node can not be lost, compared with the update rule of the optimum label of Stochastic choice, many tag update rules substantially increase robustness and the accuracy of label propagation.Finally, adopt vibration Processing for removing to the label assignment again of vibration node, solve the oscillation problem under synchronized update mode preferably, completely eliminate the randomness defect introduced due to the update sequence of node in asynchronous refresh mode, and can parallel computation be passed through, improve counting yield.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is the original state schematic diagram that the label of this method under karate club network is propagated.

Fig. 3 is the community structure schematic diagram with overlap that this method obtains under karate club network.

Embodiment

Elaborate to embodiments of the invention below, the present embodiment is implemented under premised on technical solution of the present invention, give detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

The present embodiment adopts the classical data set Zachary karate club network in community network, and this network packet is containing 34 nodes and 78 limits.Specifically comprise step as follows:

1. for each node of karate club network to be measured gives an empty label;

2. by the triangular cluster coefficient T C (e of following formulae discovery every bar limit ej _ij):

TC(e _ij)＝|N(v _i)∩N(v _j)|

Wherein: N (v _i) be node v _ithe set of neighbor node, ∩ is the operational symbol sought common ground, || be the operational symbol asking cardinal of the set, i be 1,2,3 ..., N;

3. the limit that triangular cluster coefficient is maximum is searched out;

4. all nodes in the triangular cluster on this limit being given a radix being different from other labels in network is the label of 1; Afterwards these nodes are deleted from network, obtain new network G ',

5. judge whether to exist the limit that triangular cluster coefficient is greater than 0, exist, then return step 2., otherwise the label of all nodes in now network is saved as a label array L ⁽⁰⁾, as the original state that label is propagated, enter step 6.;

5. the label array L of original state propagated by the label obtained by step ⁽⁰⁾comprise 3 kinds of different non-NULL label l altogether ₁, l ₂and l ₃, corresponding to 3 the mutually disjoint triangular cluster existed in karate club network, as shown in Figure 2, wherein each label circle represents, the node in different circle has different non-NULL labels, and blank node represents the node having sky label.

6. the propagation utilizing following formula synchronously to carry out label upgrades:

$L_i^{\left(t\right)}=\arg \underset{l}{\max }\underset{v_j\∈N\left(v_i\right)}{\mathrm{\Σ}}\mathrm{\δ}(L_j^{(t-1)},l)$

$\mathrm{\δ}(L_j^{(t-1)},l)=\left\{\begin{array}{cc}1,& l\∈L_j^{(t-1)}\\ 0,& l\∉L_j^{(t-1)}\end{array}\right.$

Wherein: node v _icarry out the label after upgrading for the t time, t is the positive integer of more than 1, N (v _i) be node v _ithe set of neighbor node, node v _ineighbor node v _jlabel after upgrading at the t-1 time, be the operational symbol of the set asking element l, the function that the l tried to achieve defines after making max obtains maximal value, when upgrading for the t time, utilizing and upgrading the label array L obtained the t-1 time ^(t-1), for the rule of all nodes in complex network G according to many tag updates, the propagation synchronously carrying out label upgrades, and is saved to new label array L ^(t);

7. label array is compared: upgrade the t time the label array L obtained ^(t)with upgrade the label array L obtained before for t-1 time ⁽¹⁾, L ⁽²⁾..., L ^(t-1)compare,

When the label array of t time is all not identical, then return step 6.;

Work as L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)middle existence and L ^(t)identical label array, then enter and show that vibration has appearred in renewal, then carry out step 8.;

As label array L ^(t-1)and L ^(t)identical, then enter step 9.

8. vibrate Processing for removing: assuming that label array L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)in there is L ^(k)and L ^(t)identical, then at label array L ^(k+1)..., L ^(t)in search out all from kth be updated to for+1 time the t time upgrade label occurred change node, at L ^(t)it is middle that the label of these nodes to be replaced to respectively the radix being different from other labels in network be the label of 1; Then step is returned 6.;

What 9. obtain network has overlapping community structure, and the node having same label element in network belongs to same community structure, and the node that label radix is greater than 1 is the lap of community structure.

Utilize this method, the label array L obtained after upgrading at the 2nd time ⁽²⁾the label array L obtained after upgrading with the 1st time ⁽¹⁾identical, so the propagation stopping label upgrades, what obtain karate club network has overlapping community structure, as shown in Figure 3.Can find out, in karate club network, co-exist in 3 community structure C ₁, C ₂and C ₃, represent with a circle respectively, the node in circle is the member node of this community structure; Node 5, node 10 and node 11 is the lap of community structure, represents with the node of black; Community structure C ₁and C ₂own node 5 and node 11 together, community C ₂and C ₃own node 10 together.

More than experiment uses typical network data collection, has been described in detail method flow of the present invention.The background knowledge of this experimental result and data set is basically identical, is divided the node ratio entering correct community structure and reaches 95.59%.In addition, modularity be one for weighing the very important index parameter of community structure quality, the modularity of community structure that this method obtains under karate club network is as calculated 0.3912, be in close proximity to theoretic maximal value 0.4020, this also demonstrates accuracy and the validity of this method.

Claims (1)

1. based on a complex network community mining method for triangular cluster multi-label, comprise the following steps: mutually disjoint triangular cluster in search network; For the initial state that the mutually different label of the Node configuration in different triangular cluster is propagated as label; According to many tag update rules, for all nodes in network, the propagation synchronously carrying out label upgrades; By the label array that obtains after upgrading with upgrade the label array obtained before and compare; If label is still in propagation, then proceed to upgrade; If label produces vibration, then proceed again after carrying out vibration Processing for removing to upgrade; If label no longer changes, then stop upgrading, obtain the community structure with overlap in network, it is characterized in that: the concrete steps of the method are as follows:

1. for each node of complex network G to be measured gives an empty label;

2. by following formulae discovery every bar limit e _ijtriangular cluster coefficient T C (e _ij):

TC(e _ij)＝|N(v _i)∩N(v _j)|

Wherein: N (v _i) be node v _ithe set of neighbor node, ∩ is the operational symbol sought common ground, || be the operational symbol asking cardinal of the set, i be 1,2,3 ..., N;

3. the limit that triangular cluster coefficient is maximum is searched out;

4. all nodes in the triangular cluster on this limit being given a radix being different from other labels in network is the label of 1; Afterwards these nodes are deleted from network, obtain new network G ',

5. judge whether to exist the limit that triangular cluster coefficient is greater than 0, exist, then return step 2., otherwise the label of all nodes in now network is saved as a label array L ⁽⁰⁾, as the original state that label is propagated, enter step 6.;

6. the propagation utilizing following formula synchronously to carry out label upgrades:

$L_i^{\left(t\right)}=\arg \underset{l}{\max }\underset{v_j\∈N\left(v_i\right)}{\mathrm{\Σ}}\mathrm{\δ}(L_j^{(t-1)},l)$

$\mathrm{\δ}(L_j^{(t-1)},l)=\left\{\begin{array}{cc}1,& l\∈L_j^{(t-1)}\\ 0,& l\∉L_j^{(t-1)}\end{array}\right.$

Wherein: node v _icarry out the label after upgrading for the t time, t is the positive integer of more than 1, N (v _i) be node v _ithe set of neighbor node, node v _ineighbor node v _jlabel after upgrading at the t-1 time, || be the operational symbol asking cardinal of the set, be the operational symbol of the set asking element l, the function that the l tried to achieve defines after making max obtains maximal value, when upgrading for the t time, utilizing and upgrading the label array L obtained the t-1 time ^(t-1), for the rule of all nodes in complex network G according to many tag updates, the propagation synchronously carrying out label upgrades, and is saved to new label array L ^(t);

7. label array is compared: upgrade the t time the label array L obtained ^(t)with upgrade the label array L obtained before for t-1 time ⁽¹⁾, L ⁽²⁾..., L ^(t-1)compare,

When the label array of t time is all not identical, then return step 6.;

Work as L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)middle existence and L ^(t)identical label array, then enter and show that vibration has appearred in renewal, then carry out step 8.;

As label array L ^(t-1)and L ^(t)identical, then enter step 9.;

8. vibrate Processing for removing: assuming that label array L ⁽¹⁾, L ⁽²⁾..., L ^(t-2)in there is L ^(k)and L ^(t)identical, then at label array L ^(k+1)..., L ^(t)in search out all from kth be updated to for+1 time the t time upgrade label occurred change node, at L ^(t)it is middle that the label of these nodes to be replaced to respectively the radix being different from other labels in network be the label of 1; Then step is returned 6.;

What 9. obtain network has overlapping community structure, and the node having same label element in network belongs to same community structure, and the node that label radix is greater than 1 is the lap of community structure.