CN105868791A - Multi-resolution community discovering method based on fuzzy clustering - Google Patents

Abstract

The invention provides a multi-resolution community discovering method based on fuzzy clustering. According to local interaction information of adjacent nodes, the structural similarity is introduced for measuring the fuzzy relation between the nodes, fuzzy transitivity of the fuzzy similarity between the nodes in a network topology is partially considered, fuzzy parameters are used for performing set cutting on a fuzzy transitivity matrix to obtain community structures under different resolutions, and therefore network communities can be discovered. Matrix transformation operation is adopted, a network community detection model based on fuzzy clustering is built, iterative optimization processes in a traditional method are reduced, the time complexity is lowered, a large number of experiments prove that the community structures in a network can be effectively revealed, the universality is strong, and the high application value is achieved; network structural analysis and community structural visualization can be effectively achieved.

Description

Multiresolution community discovery method based on fuzzy clustering

Technical field

The present invention relates to Complex Networks Analysis technical field of research, in particular it relates to a kind of based on fuzzy clustering many points Resolution community discovery method.

Background technology

Complex network is as a cross discipline widely, and it relates to computer, physics, mathematics, information science, system The ambit such as science, Network Science, is increasingly becoming the powerful tool solving challenge, and in various fields Have a wide range of applications, such as social network analysis, biological engineering, economy and finance, electric power and traffic, behavior of men analysis, Big data analysis etc..Complex network is researched and analysed, is greatly expanded it is appreciated that the breadth and depth in the world, has Major and immediate significance.In substantial amounts of complex network is studied, the research to complex network community structure, is a weight Big research focus.Dividing generally speaking, for given network structure, community's internal node has relative between community And connect more closely.Community structure characteristic in complex network is proved by substantial amounts of research.Such as, protein is handed over The research of community structure in network mutually, can analyze different known or agnoprotein matter functional modules, further appreciate that egg The complex characteristics of white matter structure.In social networks, due to the enhancing of Social Interaction, based on different interest, theme, A large amount of colonies that the features such as occupation, region are formed, community structure feature is particularly evident.Therefore, excavation network closely joins The community structure of system has important to understanding and analyzing network structure attribute, regularity of information dissemination, human society organizational structure etc. Theory significance and be widely applied value.

Community structure discovery is intended to the community structure in detection network with certain natural quality, i.e. according to certain rule, It is some modules by node division interconnective in network so that the contact of each inside modules is the densest, intermodule Connect the most sparse.Although the concept of community structure readily appreciates, but due to the multiformity of network structure and complexity, society District finds that method is the most complicated various.In the community structure research of complex network, substantial amounts of community discovery algorithm is suggested, As based on figure segmentation, hierarchical clustering, factions' filtration, centrad measurement, spectral clustering, based on modularity optimization, company frontier inspection Survey.While it is true, major part method needs priori to instruct could realize effectively division, the most do not propose one Unified measurement criterion, therefore has its limitation.According to the definition of community structure, a network can be regarded as multiple society District combines.Community structure is divided, has two key issues to need to solve: one determines that the quantity of community, right In unknown network structure, its community divides and architectural feature is unknown；Another is exactly that each community member determines, Avoid the unreasonable division of community structure.The segmentation of traditional community division method such as figure is by rigid for each node in network Be divided into a specific community, and have ignored its internal relation.In reality network, due to the complexity of network mechanism Property and multiformity, a node may belong simultaneously to multiple community, i.e. in partition process, there is the uncertainty of node Or ambiguity, the ambiguity of community structure divides closer to real network structure.

Secondly, for community structure itself, it is based on certain similarity or common trait such as social activity between its internal node The relationships such as different interest in network, hobby, theme together, this be people study starting point that community divides it One.But, the most existing community structure detection method using this similarity relationships as a kind of definitiveness or rigid degree Amount, division so can cause the unreasonable division of community. it practice, entity in live network structure is such as social networks Between similarity relation be fuzzy or probabilistic, and divide ignoring in network other heavy with a kind of certainty measure Want information.Present invention thought based on fuzzy theory proposes a kind of fuzzy division method of community structure.Solve fuzzy The basis of partition problem is exactly Fuzzy Set Theory.In the network architecture, between node, fuzzy relation emphasizes that network node is not with Same degree is under the jurisdiction of multiple community class, and non-critical is divided into a certain particular community.Meanwhile, the similarity of ambiguity The one that relation is considered as deterministic dependence is extensive.

In detecting for community structure, community effectively divides and divides two basic problems of number, and the present invention proposes a kind of base Community structure in Fuzzy clustering techniques finds method, discloses the Web Community under the conditions of different resolution simultaneously Hierarchical structure.The thought of proposition fuzzy clustering of the present invention finds the community structure in complex network, it is achieved fuzzy stroke Point, the method is based on a kind of fuzzy relational model rather than conventional graph model solves community discovery problem.

Summary of the invention

For defect of the prior art, it is an object of the invention to provide a kind of multiresolution community based on fuzzy clustering Discovery method.

The multiresolution community discovery method based on fuzzy clustering provided according to the present invention, comprises the steps:

Fuzzy switch process: set up adjacency matrix A according to network topology structure, and calculate adjacent node based on adjacency matrix A Between fuzzy relation, the fuzzy relation matrix obtained is carried out fuzzy transmitting and converting, it is thus achieved that fuzzy equivalent matrix；

Fuzzy intercepting step: be mapped in network structure by fuzzy equivalent matrix, obtain fuzzy equivalence relation class, utilizes fuzzy threshold Value intercepts this fuzzy equivalence relation class, obtains the fuzzy community structure cluster in corresponding Fuzzy Threshold level, and comes by modularity Evaluate the Clustering Effect of fuzzy community.

Preferably, described fuzzy switch process includes:

Step M1: network to be analyzed is set up the adjacency matrix A of network, is numbered node according to node sequence, compiles Number from the beginning of 1, building the N rank square formation that element is 0 or 1, wherein N is the total number of network node；

Step M2: obtain the similarity between adjacent node, is converted into fuzzy resembling relation by deterministic syntopy, Realization will abut against matrix A and is converted to fuzzy relationship matrix r；

Step M3: for the similarity between tolerance nonneighbor node further, fuzzy relationship matrix r is carried out fuzzy transmission and becomes Change, make internodal similarity reach consistent stability；

Step M4: the uniformly convergent fuzzy relation obtained by fuzzy transmission function, sets up fuzzy transfer matrix, and Obtain fuzzy equivalent matrix.

Preferably, in described step M2, according to the structural similarity metric algorithm of definition obtain between adjacent node similar Degree, the computing formula of described structural similarity metric algorithm is as follows:

$s(u,v)=\frac{{\Σ}_{x\∈\mathrm{\Γ}\left(u\right)\∩\mathrm{\Γ}\left(v\right)}w(u,x)\·w(v,x)}{\sqrt{{\Σ}_{x\∈\mathrm{\Γ}\left(u\right)}{w}^2(u,x)}\·\sqrt{{\Σ}_{x\∈\mathrm{\Γ}\left(v\right)}{w}^2(v,x)}}$

In formula, u, v are respectively the arbitrary node in set of network nodes, and Γ () represents the adjacent node set of certain node, Γ (u) Representing the adjacent node set of node u, Γ (v) represents the adjacent node set of node v, and w () represents and connects between certain two node The weight on limit, (u, x) connects the weight on limit to w between expression node u and node x, (v x) represents and connects between node v and node x w The weighting structure similarity on limit, s (u, v) ∈ [0,1]；For connecting the weight on limit between undirected arbitrary node without weighting network W ()=1, then the formula of structural similarity metric algorithm is further simplified as following form:

$s(u,v)=\frac{|\mathrm{\Γ}\left(u\right)\∩\mathrm{\Γ}\left(v\right)|}{\sqrt{\left|\mathrm{\Γ}\left(u\right)\right|\·\left|\mathrm{\Γ}\left(v\right)\right|}}.$

Preferably, the fuzzy transmission transforming function transformation function in described step M3 is as follows:

$t\left(R\right)={\∪}_{k=1}^n{R}^k;$

In formula, the dimension of n representing matrix, n=| V |, V represent network node sequence vector, and R represents fuzzy relation matrix, T (R) represents fuzzy equivalence relation, and ∪ represents that fuzzy relation synthesizes computing, and k represents the number of times of fuzzy relation synthesis computing, its MeetFuzzy equivalence relation meets

Preferably, described fuzzy equivalent matrix, have the property that

Character 1: symmetry；For Undirected networks structure, internodal fuzzy relation meets symmetry；I.e. node i is to joint Point j fuzzy relation r (i, j) be equivalent to node j to node i fuzzy relation r (j, i)；

Character 2: reflexivity；In fuzzy relation matrix, any node is 1 to the fuzzy relation perseverance of self, i.e. and r (i, i)=1；

Character 3: transitivity；For the fuzzy equivalent matrix through fuzzy transmission conversion, meet

Preferably, described fuzzy intercepting step includes:

Step N1: fuzzy equivalence relation matrix and the network node one_to_one corresponding that will obtain, obtains fuzzy equivalence relation class, institute State fuzzy equivalence relation class and be equivalent to the hierarchical clustering tree construction of network；

Step N2: selected arbitrary Fuzzy Threshold ε ∈ [0,1], intercepts fuzzy equivalence relation class, obtains the mould of correspondence Stick with paste community division result；

Step N3: calculate the module angle value of corresponding fuzzy community division result；

Step N4: regulation Fuzzy Threshold ε, obtains the community structure under the conditions of different resolution.

Preferably, in described step N3, the computing formula of modularity value Q is as follows:

$Q=\underset{i}{\Σ}\[e_{ii}-a_i^2)\]$

In formula, i represents the community's quantity in network division, e_iiRepresent that the quantity connecting limit between i-th community internal node accounts for whole The ratio of individual network edge number, a_iRepresent the ratio of one section of company's limit quantity being connected with i-th community interior joint.

Compared with prior art, the present invention has a following beneficial effect:

1, the present invention is on the basis of legacy network community discovery, uses fuzzy clustering method to realize community structure Effectively divide；Unlike existing algorithm, similarity relation between its Fuzzy processing node and community rather than one determine The hard plot of property, thus avoid the unreasonable division of network structure.

2, the present invention achieves the community structure division under different resolution in the control to Fuzzy strategy, enters one Step has excavated the network structure characteristic of complex network.

3, the present invention is based on fuzzy behaviour, in conjunction with the partial structurtes information of node, it is proposed that effective structural similarity degree Metering method, improves reasonability and reliability that community structure divides.

Accompanying drawing explanation

By the detailed description non-limiting example made with reference to the following drawings of reading, the further feature of the present invention, Purpose and advantage will become more apparent upon:

Fig. 1 is method provided by the present invention and additive method performance comparison figure on GN network.

Fig. 2 is method provided by the present invention and additive method performance comparison figure on LFR network.

Fig. 3 is the present invention scattergram to the Fuzzy Threshold value on above-mentioned GN network.

Fig. 4 is the present invention scattergram to the Fuzzy Threshold value on above-mentioned LFR network.

Fig. 5 (a) is a kind of division result schematic diagram that the present invention analyzes a live network, and Fig. 5 (b) is another kind of Division result schematic diagram.

Fig. 6 is that the present invention carries out Web Community's scattergram that fuzzy clustering obtains under different resolution to above-mentioned live network.

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is described in detail.Following example will assist in those skilled in the art Member is further appreciated by the present invention, but limits the present invention the most in any form.It should be pointed out that, the common skill to this area For art personnel, without departing from the inventive concept of the premise, it is also possible to make some changes and improvements.These broadly fall into Protection scope of the present invention.

The multiresolution community discovery method based on fuzzy clustering provided according to the present invention, comprises the steps:

Fuzzy switch process: set up adjacency matrix A according to network topology structure, and calculate adjacent node based on adjacency matrix A Between fuzzy relation, the fuzzy relation matrix obtained is carried out fuzzy transmitting and converting, it is thus achieved that fuzzy equivalent matrix；

Fuzzy intercepting step: be mapped in network structure by fuzzy equivalent matrix, obtain fuzzy equivalence relation class, utilizes fuzzy threshold Value intercepts this fuzzy equivalence relation class, obtains the fuzzy community structure cluster in this Fuzzy Threshold level, and comments by modularity Valency obscures the Clustering Effect of community.

Described fuzzy switch process includes:

Step M1: network to be analyzed is set up the adjacency matrix A of network, is numbered node according to node sequence, compiles Number from the beginning of 1, building the N rank square formation that element is 0 or 1, wherein N is the total number of node；

Step M2: obtain the similarity between adjacent node, by deterministic according to the structural similarity metric algorithm of definition Syntopy is converted into fuzzy resembling relation, it is achieved will abut against matrix A and is converted to fuzzy relationship matrix r；

Step M3: for the similarity between tolerance nonneighbor node further, fuzzy relationship matrix r is carried out fuzzy transmission and becomes Change, make internodal similarity reach consistent stability；

Step M4: the uniformly convergent fuzzy relation obtained by fuzzy transmission function, sets up fuzzy transfer matrix, and Obtain fuzzy equivalent matrix.

Structural similarity metric algorithm in described step M2 is as follows:

$s(u,v)=\frac{{\Σ}_{x\∈\mathrm{\Γ}\left(u\right)\∩\mathrm{\Γ}\left(v\right)}w(u,x)\·w(v,x)}{\sqrt{{\Σ}_{x\∈\mathrm{\Γ}\left(u\right)}{w}^2(u,x)}\·\sqrt{{\Σ}_{x\∈\mathrm{\Γ}\left(v\right)}{w}^2(v,x)}}$

In formula, u, v are respectively the arbitrary node in set of network nodes, and Γ () represents the adjacent node set of certain node, Γ (u) Representing the adjacent node set of node u, Γ (v) represents the adjacent node set of node v, and w () represents and connects limit between certain node Weight, w (u, x) represents and connects the weight on limit between node u, w (v, x) represents and connects the weighting structure similarity on limit between node v, s(u,v)∈[0,1]；For connecting weight w ()=1 on limit, then structural similarity degree between undirected arbitrary node without weighting network The formula of quantity algorithm is further simplified as following form:

$s(u,v)=\frac{|\mathrm{\Γ}\left(u\right)\∩\mathrm{\Γ}\left(v\right)|}{\sqrt{\left|\mathrm{\Γ}\left(u\right)\right|\·\left|\mathrm{\Γ}\left(v\right)\right|}}.$

Fuzzy transmission transforming function transformation function in described step M3 is as follows:

$t\left(R\right)={\∪}_{k=1}^n{R}^k;$

In formula, the dimension of n representing matrix, its satisfied=| V | (V represents network node sequence), R represents fuzzy relation square Battle array, t (R) represents fuzzy equivalence relation, and ∪ represents that fuzzy relation synthesizes computing, and k represents the number of times of fuzzy relation synthesis computing, It meetsFuzzy equivalence relation meets

Described fuzzy equivalent matrix, has the property that

Character 1: symmetry；For Undirected networks structure, internodal fuzzy relation meets symmetry；I.e. node i is to joint Point j fuzzy relation r (i, j) be equivalent to node j to node i fuzzy relation r (j, i)；

Character 2: reflexivity；In fuzzy relation matrix, any node is 1 to the fuzzy relation perseverance of self, i.e. and r (i, i)=1.

Character 3: transitivity；For the fuzzy equivalent matrix through fuzzy transmission conversion, meet

Described fuzzy intercepting step includes:

Step N1: fuzzy equivalence relation matrix and the network node one_to_one corresponding that will obtain, obtains fuzzy equivalence relation class, institute State fuzzy equivalence relation class and be equivalent to the hierarchical clustering tree construction of network；

Step N2: selected arbitrary Fuzzy Threshold ε ∈ [0,1], intercepts fuzzy equivalence relation class, obtains the mould of correspondence Stick with paste community division result；

Step N3: calculate the module angle value of corresponding fuzzy community division result；

Step N4: regulation Fuzzy Threshold ε, obtains the community structure under the conditions of different resolution.

In described step N3, the computing formula of modularity value Q is as follows:

$Q=\underset{i}{\Σ}\[e_{ii}-a_i^2)\]$

In formula, i represents the community's quantity in network division, e_iiRepresent that the quantity connecting limit between community's i internal node accounts for whole net The ratio of network limit number, a_iRepresent the ratio of one section of company's limit quantity being connected with community's i interior joint.Usually, module angle value is more Greatly, represent that the effect that Web Community divides is the best.

Specifically, comprise the steps:

Step S1: set up the adjacency matrix A of network according to network structure information, according to node sequence, node is numbered, Numbering, from the beginning of 1, builds N rank square formation, and wherein N is the total number of node, directly connects limit with 1 if had between two nodes Represent, be otherwise 0；

Step S2: conversion fuzzy relation.The similarity between structural similarity metric calculation adjacent node according to definition, Deterministic linking relationship is converted into fuzzy resembling relation, it is achieved will abut against matrix A and be converted to fuzzy relationship matrix r；

Step S3: fuzzy transmitting and converting.For the similarity between tolerance nonneighbor node further, fuzzy relationship matrix r is entered Row transmission conversion, makes internodal similarity reach consistent stability, to R matrix by fuzzy transfer function by fuzzy Transmission conversion；

Step S4: fuzzy equivalent matrix；According to the uniformly convergent fuzzy relation obtained by fuzzy transferometer Set up fuzzy equivalent matrix；

Step S5: fuzzy equivalence relation class, the fuzzy equivalence relation matrix that will obtain, with network node one_to_one corresponding, obtain Fuzzy equivalence relation class, this equivalence class is equivalent to the hierarchical clustering tree construction of network；

Step S6: selected arbitrary Fuzzy Threshold ε ∈ [0,1], intercepts fuzzy equivalence relation class, obtains the fuzzy of correspondence Colony divides；

Step S7: define according to above-mentioned modularity, calculates the module angle value that corresponding fuzzy community divides, module angle value The biggest, illustrate that Web Community divides effect the best；

Step S8: regulation Fuzzy Threshold ε, obtains the community structure under the conditions of different resolution.

By describe in detail the effectiveness of offer method and extensibility, the present invention has carried out the following examples by experiment.

1) experiment condition: CPU Intel Pentium Dual-Core 2.0-GHz, RAM 4.00GB, Windows 7 Operating system, simulation software RStudio.

2) experimental subject:

Synthetic network and real world network are chosen in experiment respectively.

Synthetic network

Further, Girvan and Newman in 2002 at paper " Community structure in social and biological networks”Girvan M,Newman M.E.Proceedings of the National Academy of Sciences of the United States of America.2002,99 (12): 7821-6. (manually generated network uses GN respectively Baseline network and LFR baseline network) middle proposition.This network is formed community's knot of four equal scales by 128 nodes Structure, node has identical degree and is distributed, and the out-degree of node and in-degree scalable, it represents node with hybrid parameter μ Going out the in-degree ratio fog-level with adjustment network, μ value is the biggest, and the boundary between Web Community is the fuzzyyest.

Lancichinetti et al. proposed (Lancichinetti A, Fortunato S, Radicchi F.Benchmark in 2008 graphs for testing community detection algorithms.Physical Review E.2008,78(4):046110.) LFR baseline network；It practice, LFR baseline network is the extension of GN baseline network, that reflects node degree distribution and The homogeneity of community structure scale distribution, i.e. node degree distribution and community's scale meet power-law distribution so that web results is more Close to live network.In order to evaluate the performance of inventive method, standard mutual information (NMI) is used to measure division result. If NMI value is closer to 1, illustrate that the community structure found is closer to real community structure.

Presently disclosed method represents with Strsim in an experiment.Meanwhile, for embodying its impact of performance, this method and its He compares by the community discovery method of several classics.These methods include: Pons et al. in 2005 at " 20th International Symposium on Computer and Information Sciences " on " Computing that delivers Communities in large networks using random walks " the middle Walktrap method proposed, Vincent et al. " the Fast unfolding of communities in delivered on " Journal of Statistical Mechanics " in 2008 Large networks " in propose BGLL method, and Rosvall and Bergstrom in 2008 at " Proceedings Of the National Academy of Sciences of the United States of America " on " the Maps of that delivers Random walks on complex networks reveal community structure " the middle Infomap method proposed.

The simulation experiment result based on GN baseline network is as shown in Figure 1.When mixed coefficint is less than 0.4, all methods Can effectively detect real community structure, i.e. NMI=1.Along with mixed coefficint is gradually increased, the community of each method Structure recognition ability presents and declines in various degree.As it can be seen, when mixed coefficint is more than 0.When 5, Infomap method Community detection ability drastically drops to 0, and the performance of Walktrap and BGLL method also gradually reduces, and the present invention is carried Performance for method but presents stable.Reason is that this method takes the phase that a kind of local searching strategy comes between node metric Like degree, in the case of Web Community's obscurity boundary, still can identify that the node of arest neighbors keeps certain identification ability. It is clear that method provided by the present invention has clear superiority for the network structure that community boundary is fuzzy.

The simulation experiment result based on LFR baseline network is as shown in Figure 2.In LFR network, node degree distribution, society District's quantity and community's scale all change.When mixed coefficint is not more than 0.5, all methods are to the network society in LFR network Plot structure has good identification ability.Along with mixed coefficint constantly increases, the performance of each method also presents in various degree Decline.When mixed coefficint is more than 0.6, Infomap method None-identified goes out community structure therein (NMI=0), And the performance of additive method is gradually lowered.As it can be seen, when mixed coefficint is 0.6, BGLL method can obtain relatively Good effect, but, when Web Community border more obscures, its performance is poor compared with Walktrap and Strsim method.And Presently disclosed method still can keep certain identification ability when mixed coefficint constantly reduces.The further body of this experiment Effectiveness and the stability of this method are showed.

For the fuzzy clustering of network structure, Fuzzy Threshold is chosen and is evaluated by this method, and obtains Fuzzy Threshold Optimum experience interval, as shown in Figure 3 and Figure 4.Fig. 3 is that this method obscures in difference on GN baseline network NMI value distribution under coefficient condition.This distribution presents stepped distribution, and under different mixed coefficints, presents Similar trend, is finally reached steady statue, and this is consistent with above-mentioned experimental result.As it can be seen, when Fuzzy Threshold value When scope is [0.2,0.4], this method can obtain optimal result.Meanwhile, by analysis chart 4 it can be seen that work as mixed stocker When number is less than 0.5, Fuzzy Threshold value distribution of results difference is bigger.When mixed coefficint is more than 0.5, present similar Trend, and reach stable result.Relatively it is found that when Fuzzy Threshold span is [0.2,0.4], this method Optimal result can be obtained.

Real world network

Real world network in this experiment selects Zachary karate club social networks.This network is widely used in survey The validity and reliability of examination community detection algorithm.This network is to the society's friendship between this clubbite based on Zachery Carry out the investigation up to two years and observation mutually, and construct a friendship with 78 limits of 34 clubbites Network mutually.During observing, owing to the suggestion between Club Management person (node 1) and coach's (node 33) is divided Discrimination, final club splits into two less community structures.This method is applied to the result of this network as shown in Figure 5. Figure only gives two of which division result.When Fuzzy Threshold is adjusted, can obtain under different resolution The module angle value of community structure, its community's number and partition structure is as shown in Figure 6.When this network obtains 4 community structure, Modularity obtains maximum.

In an experiment, institute of the present invention extracting method can effectively detect the separating phenomenon in network structure.Test result indicate that, Two groups with obvious community structure are detected, and as shown in Fig. 5 (a), different Web Communities is with different joints Point shape representation.By regulation fuzzy parameter, the community structure of higher resolution can be obtained.As shown in Fig. 5 (b), This network is divided into 3 communities, respectively with different shape representations in figure.In this division, due to tight between node Similarity, node 25,26,29 and 32 is extracted as a single community.Meanwhile, by regulation clustering parameter ε, The community of the smaller particle size being closely connected within community is found.When choosing bigger blur parameter value, this network quilt Being divided into 4 community structures, it is consistent with the result of the CNM algorithm partition that Clauset et al. proposes.Closed by regulation Suitable parameter value, the community structure of varying number is extracted, and corresponding different module angle value, as shown in Figure 6.Work as quilt A modularity of maximum is had when being divided into 4 community structures, and the division of 2 communities corresponding to real network non-optimal, Therefore, when modularity is on close level, suitably should select according to more effective criterion.And in this experiment, according to being carried Going out method, its community's partition structure is accurate and effective.

Above the specific embodiment of the present invention is described.It is to be appreciated that the invention is not limited in Stating particular implementation, those skilled in the art can make a variety of changes within the scope of the claims or revise, This has no effect on the flesh and blood of the present invention.In the case of not conflicting, in embodiments herein and embodiment Feature can arbitrarily be mutually combined.

Claims (7)

1. a multiresolution community discovery method based on fuzzy clustering, it is characterised in that comprise the steps:

Fuzzy switch process: set up adjacency matrix A according to network topology structure, and calculate adjacent node based on adjacency matrix A Between fuzzy relation, the fuzzy relation matrix obtained is carried out fuzzy transmitting and converting, it is thus achieved that fuzzy equivalent matrix；

Fuzzy intercepting step: be mapped in network structure by fuzzy equivalent matrix, obtain fuzzy equivalence relation class, utilizes fuzzy threshold Value intercepts this fuzzy equivalence relation class, obtains the fuzzy community structure cluster in corresponding Fuzzy Threshold level, and comes by modularity Evaluate the Clustering Effect of fuzzy community.

Multiresolution community discovery method based on fuzzy clustering the most according to claim 1, it is characterised in that institute State fuzzy switch process to include:

Step M1: network to be analyzed is set up the adjacency matrix A of network, is numbered node according to node sequence, compiles Number from the beginning of 1, building the N rank square formation that element is 0 or 1, wherein N is the total number of network node；

Step M2: obtain the similarity between adjacent node, is converted into fuzzy resembling relation by deterministic syntopy, Realization will abut against matrix A and is converted to fuzzy relationship matrix r；

Step M3: for the similarity between tolerance nonneighbor node further, fuzzy relationship matrix r is carried out fuzzy transmission and becomes Change, make internodal similarity reach consistent stability；

Step M4: the uniformly convergent fuzzy relation obtained by fuzzy transmission function, sets up fuzzy transfer matrix, and Obtain fuzzy equivalent matrix.

Multiresolution community discovery method based on fuzzy clustering the most according to claim 2, it is characterised in that institute State in step M2, obtain the similarity between adjacent node, described structure phase according to the structural similarity metric algorithm of definition As follows like the computing formula of property metric algorithm:

$s(u,v)=\frac{{\mathrm{\Σ}}_{x\∈\mathrm{\Γ}\left(u\right)\∩\mathrm{\Γ}\left(v\right)}w(u,x)\·w(v,x)}{\sqrt{{\mathrm{\Σ}}_{x\∈\mathrm{\Γ}\left(u\right)}{w}^2(u,x)}\·\sqrt{{\mathrm{\Σ}}_{x\∈\mathrm{\Γ}\left(v\right)}{w}^2(v,x)}}$

In formula, u, v are respectively the arbitrary node in set of network nodes, and Γ () represents the adjacent node set of certain node, Γ (u) Representing the adjacent node set of node u, Γ (v) represents the adjacent node set of node v, and w () represents and connects between certain two node The weight on limit, (u, x) connects the weight on limit to w between expression node u and node x, (v x) represents and connects between node v and node x w The weighting structure similarity on limit, s (u, v) ∈ [0,1]；For connecting the weight on limit between undirected arbitrary node without weighting network W ()=1, then the formula of structural similarity metric algorithm is further simplified as following form:

$s(u,v)=\frac{|\mathrm{\Γ}\left(u\right)\∩\mathrm{\Γ}\left(v\right)|}{\sqrt{\left|\mathrm{\Γ}\left(u\right)\right|\·\left|\mathrm{\Γ}\left(v\right)\right|}}.$

Multiresolution community discovery method based on fuzzy clustering the most according to claim 2, it is characterised in that institute State the fuzzy transmission transforming function transformation function in step M3 as follows:

$t\left(R\right)={\∪}_{k=1}^n{R}^k;$

In formula, the dimension of n representing matrix, n=| V |, V represent network node sequence vector, and R represents fuzzy relation matrix, T (R) represents fuzzy equivalence relation, and U represents that fuzzy relation synthesizes computing, and k represents the number of times of fuzzy relation synthesis computing, its MeetFuzzy equivalence relation meets

Multiresolution community discovery method based on fuzzy clustering the most according to claim 2, it is characterised in that institute State fuzzy equivalent matrix, have the property that

Character 1: symmetry；For Undirected networks structure, internodal fuzzy relation meets symmetry；I.e. node i is to joint Point j fuzzy relation r (i, j) be equivalent to node j to node i fuzzy relation r (j, i)；

Character 2: reflexivity；In fuzzy relation matrix, any node is 1 to the fuzzy relation perseverance of self, i.e. and r (i, i)=1；

Character 3: transitivity；For the fuzzy equivalent matrix through fuzzy transmission conversion, meet

Multiresolution community discovery method based on fuzzy clustering the most according to claim 1, it is characterised in that Described fuzzy intercepting step includes:

Step N1: fuzzy equivalence relation matrix and the network node one_to_one corresponding that will obtain, obtains fuzzy equivalence relation class, institute State fuzzy equivalence relation class and be equivalent to the hierarchical clustering tree construction of network；

Step N2: selected arbitrary Fuzzy Threshold ε ∈ [0,1], intercepts fuzzy equivalence relation class, obtains the mould of correspondence Stick with paste community division result；

Step N3: calculate the module angle value of corresponding fuzzy community division result；

Step N4: regulation Fuzzy Threshold ε, obtains the community structure under the conditions of different resolution.

Multiresolution community discovery method based on fuzzy clustering the most according to claim 6, it is characterised in that In described step N3, the computing formula of modularity value Q is as follows:

$Q=\underset{i}{\Σ}\[e_{ii}-a_i^2)\]$

In formula, i represents the community's quantity in network division, e_iiRepresent that the quantity connecting limit between i-th community internal node accounts for whole The ratio of individual network edge number, a_iRepresent the ratio of one section of company's limit quantity being connected with i-th community interior joint.