CN103810260A - Complex network community discovery method based on topological characteristics - Google Patents

Complex network community discovery method based on topological characteristics Download PDF

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CN103810260A
CN103810260A CN201410037855.1A CN201410037855A CN103810260A CN 103810260 A CN103810260 A CN 103810260A CN 201410037855 A CN201410037855 A CN 201410037855A CN 103810260 A CN103810260 A CN 103810260A
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corporations
network
degree
membership
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CN103810260B (en
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周红芳
段文聪
王心怡
何馨依
郭杰
张国荣
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Xian University of Technology
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Abstract

Provided is a complex network community discovery method based on topological characteristics. The complex network community discovery method includes the steps of 1 initialization, wherein each node in a network is used as an independent community, if n nodes exist in the network, n initialization communities exist, the criticality of each node is zero, and the affiliation depends on edge connection strength; 2 edge connection strength calculation, wherein the edge connection strength between all connected nodes is calculated, namely the number of triangles formed by every two nodes with edge connection is calculated; 3 iteration, wherein the following operations are conducted on each node in sequence, firstly, a node is deleted from the community where the node is located, the affiliation between the node and the communities is calculated, and the node is included into the community with the maximum affiliation. According to the complex network community discovery method, initial partition does not need to be conducted on data sets, the number of clusters does not need to be input, the precision is high, and the complex network community discovery method is simple and easy to implement.

Description

Complex network community discover method based on topological property
Technical field
The invention belongs to data digging method technical field, relate to a kind of Web Community's discover method based on topological property.
Background technology
Along with the further investigation of physical significance and the mathematical characteristic of complex network character, it is found that at most complex network and all there is common character, i.e. a community structure.That is to say, whole network can be divided into several corporations, between these corporations' internal nodes, closely connects, and connects comparatively sparse between corporations.Research shows, typical complex network all has obvious community structure as internet, social relation network, reference citation network, protein interaction network etc.Excavating the corporations in network, is all very important for awareness network structure and analysis network characteristic.
The research of community structure in complex network has been had to very long history.At present, the method based on hierarchical clustering is suggested and becomes gradually the main stream approach of research.Hierarchical clustering is similarity or the intensity of the connection based between each node, nature network be divided into each subgroup.Still remove limit according to adding limit from network, hierarchical clustering method can be divided into: splitting method and condensing method.
Except community discovery, be the key node in discovering network for the another kind of research method of complex network.The node that ectocine has different topology characteristic can cause net list to reveal robustness or fragility in various degree.Therefore, be necessary to study the key node in network.Conventionally adopt the centrality of node to estimate the size of (centrality measure) measurement node capability of influence in network, can understand the ability of this node acquisition, control information and resource by the topological property of network.The discovery of community discovery and key node is often by independently of each other for Analysis of Complex network.Yizhou Sun etc. has proposed a kind of new thinking, and they combine the cluster of nodes with the sequence of node.That is to say, the discovery of community discovery and key node can be carried out simultaneously, and complements each other.The Rankclus algorithm of the propositions such as Yizhou Sun is successfully used to the analysis of computer science document network.
But Rankclus algorithm is for Heterogeneous Information network (heterogeneous information network), and this algorithm need to specify cluster numbers in advance, and need to carry out randomly initial division, thereby causes the unstable of cluster result.
Summary of the invention
The object of this invention is to provide a kind of complex network community discover method based on topological property, solved the unsettled problem of cluster result that prior art exists.
The technical solution adopted in the present invention is that the complex network community discover method based on topological property, comprising:
Step 1, initialization; Using the each node in network as corporations independently, if there be n node in network, so just there are n initialization corporations, the key of each node is 0, degree of membership depends on limit strength of joint;
Step 2, calculates limit strength of joint; Calculate the limit strength of joint between all connected nodes, the leg-of-mutton number that two nodes that namely calculating has limit to be connected form;
Step 3, iteration; In order each node is carried out to following operation: first, a node is deleted from its place corporations, calculated the degree of membership of this node and each corporations, the corporations by node division to degree of membership maximum.
In step 3, after node is divided into new corporations, the center degree of coupled node may change, and need to recalculate the key of them, the leg-of-mutton number that can form; Afterwards, next node is carried out to same operation; When having traveled through all nodes, one time iteration finishes; Through iteration repeatedly, the ownership of each node will no longer change, and algorithm stops.
Limit strength of joint is for weighing two similarities between connected node, using s ijrepresent the strength of joint between node i and node j, s ijequal to comprise the leg-of-mutton number that node i and node j form in networking.
Key, be to weigh node significance level in corporations under it, use c jrepresent node j key in corporations under it, c jequal in corporations, to comprise the leg-of-mutton number of node j under node j.
Degree of membership is the criterion of node division, i.e. relation between node and each corporations; Degree of membership computing formula is as follows:
A ( i , g ) = Σ j ∈ g ( ( 1 + s ij ) . ( 1 + c j r ) ) - - - ( 1 )
Wherein A (i, g) is with regard to the degree of membership of representation node i and the g of corporations, s ijthe limit strength of joint of node j in representation node i and the g of corporations, c jkey in the g of corporations of representation node j, r is coefficient, is preferably 10.
The present invention has following beneficial effect:
1, the present invention utilizes the topological property of each node in network, the critical information of node is used for to community discovery, by the Clustering features on limit between connected node and each node, the central characteristics in corporations is combined into a new measurement index-degree of membership, because 1. the present invention has considered the critical information in corporations of node, these information contribute to divide belonging to fuzzy node, 2. adopt the process of loop iteration that each node is divided in order, therefore, improved the accuracy of cluster.In contrast to BGLL algorithm, CNM algorithm, MOGA-Net algorithm, the present invention has higher accuracy on four Network data sets (Amazon politics book network, university's league football match network that karate club relational network, dolphin relational network, Kreb provide).
2. for the network of general structure, time complexity of the present invention approaches linear, the results show, and discover method of the present invention is significantly less than CNM algorithm the working time on large scale network.
3. the present invention does not need data set to carry out initial division, does not need to input cluster numbers yet, simply, easily go.
Accompanying drawing explanation
Fig. 1 is discover method of the present invention and BGLL algorithm, CNM algorithm, the experiment effect comparison diagram of MOGA-Net algorithm on four complex network data sets (Amazon politics book network, university's league football match network that karate club relational network, dolphin relational network, Kreb provide);
Fig. 2 uses discover method of the present invention to carry out the result of ten experiments after random alignment node sequence, the number order of node is all different each time;
Fig. 3 is a simple network being made up of six nodes, can be divided into left and right Liang Ge corporations;
The detailed process of iteration for the first time when Fig. 4 is the network of discover method of the present invention in analysis chart 3;
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.
Related definition in the present invention is as follows:
Define 1 limit strength of joint: being for weighing two similarities between connected node, is mainly according to the Clustering features of these two connected nodes in network.Clustering features, refers to the similarity between two node topology structure attributes in network, and the general topological structure attribute adopting is the quantity of two common connected nodes of node.Use s ijrepresent the strength of joint between node i and node j, s ijequal to comprise the leg-of-mutton number that node i and node j form in networking.
Define 2 key: being to weigh node significance level in corporations under it, is mainly the central characteristics in corporations according to this node.Central characteristics, refers to the significance level on a node topology structure attribute in network, the general topological structure attribute degree of being adopting, the quantity of the node being connected with this node.The topological structure attribute that the present invention adopts is the leg-of-mutton quantity that node forms.Use c jrepresent node j key in corporations under it, c jequal in corporations, to comprise the leg-of-mutton number of node j under node j.
Define 3 degree of membership: it is the criterion as node division, i.e. relation between node and each corporations.In the present invention, calculate the degree of membership of each node and each corporations, the corporations by node division to degree of membership maximum.Computing formula is as follows:
A ( i , g ) = Σ j ∈ g ( ( 1 + s ij ) . ( 1 + c j r ) ) - - - ( 1 )
Wherein A (i, g) is with regard to the degree of membership of representation node i and the g of corporations, s ijthe limit strength of joint of node j in representation node i and the g of corporations, c jkey in the g of corporations of representation node j, r is a coefficient, for reducing c jinfluence power.The present invention divides according to limit strength of joint between node, and therefore node key as supplementary set coefficient r and reduce the critical impact of node.Experimental result shows, in the time that r is set to 10, to have good effect.
The present invention mainly comprises 3 steps:
Step 1 initialization
The first step of the present invention is initialization, and the each node in network is as corporations independently.If there be n node in network, so just there are n initialization corporations.The key of each node is 0, and degree of membership only depends on limit strength of joint.
Step 2 is calculated limit strength of joint
Second step is the limit strength of joint calculating between all connected nodes, the leg-of-mutton number that two nodes that namely calculating has limit to be connected form.
Step 3 iteration
The 3rd step is the process of iteration, in order each node is carried out to following operation.First, given node is deleted from its place corporations, the leg-of-mutton number that the node being connected with deleted node in corporations forms may reduce, and need to recalculate the key of them.Suppose that in certain corporation, node i and node j have n common connected node in corporations, so node i deleted after, the key of node j will reduce n.Calculate the degree of membership of this node and each corporations, the corporations by node division to degree of membership maximum.After node is divided into new corporations, the center degree of coupled node may change, and need to recalculate the key of them, the leg-of-mutton number that can form.Afterwards, next node is carried out to same operation.When having traveled through all nodes, one time iteration finishes.Through iteration repeatedly, in general 3 to 5 times, the ownership of each node will no longer change, and algorithm stops.
The element of alternative technical characteristic, in the present invention, the key of limit strength of joint and node is mainly to rely on the triangle in network to weigh, and is similar to the convergence factor in topological property.Convergence factor is applicable to community network, because there is a large amount of triangles in this class network.Except convergence factor, can use the topological property of other types to replace, conventional topological property also has:
1. betweenness (betweenness): according to intuition and experience, if on the many paths in network of node or limit, it also should have certain special status at network so, because whether its existence likely has influence on the relation between other node, even can have influence on other node by the transmission of controlling or twist information.Betweenness is defined as the number through present node or limit in all shortest paths of network, and the hinge degree of its reflection node or present position in particular network topological structure, limit, can distinguish the inside and outside limit of module effectively by it.The circulation of much information, resource and transmit and must just be able to other nodes in shortest path (or shortcut) arrival network by central hub node.
2. the degree of approach (closeness): if node relies on other node in network, the size of so this degree of dependence also can reflect its Central Position on topological structure in some sense.On information is transmitted, non-core node must rely on other more node, core node less; Just lower with the dependence of the more approaching node of other node.The degree of approach is exactly to this dependent tolerance, the level of intimate of its expression present node and all other node annexations, and it is inversely proportional to this node and other nodal distance sum.General take the distance between node as foundation on concrete measurement, if all very short (apart from sum minimum) of the distance of all other nodes in node and network, its degree of approach is just high so, and therefore this is estimated and can reflect that to a certain extent node is in the overall situation or center degree on the whole.
3. information degree (information): betweenness is only considered the shortest path between node, and other path may obtain or transmission of information aspect also have its importance.Information degree is based on being delivered in the information between any two nodes in connected network, and it weighs the weighted array of present node to the path of all other nodes of network.Newman thinks that it is actually the another kind of degree of approach, be to measure harmonic average length take a node as the path of end points in essence, if this node is connected with other node by many short paths, mean the little and information degree (degree of approach) of its average path length greatly.
The present invention, by permeate a new index-degree of membership of two kinds of topological property-Clustering features and central characteristics, is applied to the centrality information of key node in the middle of community discovery.The Clustering features of two nodes is defined as intensity-Bian strength of joint (definition 1) on the limit that connects these two nodes.Node topological structure centrality in corporations under it is defined as key (definition 2).
What limit strength of joint reflected is in network, be connected two the structural relations of node topology, the namely topologicaies property on limit.The widespread use in splitting-up method of the topological property on limit.In GN algorithm, divide network by the limit that removes betweenness maximum, but the time complexity of calculating betweenness is higher, this is also GN algorithm greatest problem.In Radicchi fast algorithm, adopt limit convergence factor to replace betweenness.Limit convergence factor is defined as the actual leg-of-mutton number that comprises this limit in network and the ratio of leg-of-mutton number that likely comprises this limit, and algorithm complex obviously reduces.That is to say, the importance on a limit depends on the leg-of-mutton number that comprises this limit.Triangle in corporations is more, and the convergence factor on limit is larger.The present invention adopts leg-of-mutton number that limit can form in the network index as this limit strength of joint, and the leg-of-mutton number that comprises a certain limit in network is more, just thinks that the strength of joint on this limit is just larger.Also can be understood as: if two nodes are connected, and these two nodes have multiple common neighbor nodes, think that the connection between these two nodes is stronger, and these two nodes have stronger Clustering features.
Network key node recognition method is in the past mainly according to the degree of node or convergence factor, a node degree refers to the interstitial content being connected with this node, and node rendezvous coefficient refers to the leg-of-mutton number that the leg-of-mutton number that comprises this node in network can form divided by the coupled node of this node.Using the leg-of-mutton number that adopts node to form in corporations as the critical index of node, those nodes simultaneously with larger degree and larger convergence factor can be judged as the key node in corporations in the present invention.Adopt this index can guarantee that node in the dense subgraphs such as full even subgraph all has higher key.In the dense subgraph that even summation subgraph and density are larger entirely, all have a large amount of triangles, so limit connection is wherein stronger, then guarantees the key also stronger of node, guaranteed that the corporations that mark off have larger limit density.
Tradition agglomerative algorithm is with calculating someway the similarity between each node, then from the highest node of similarity to, be n and add limit in original abortive haul network that the number on limit is 0 toward a nodes.According to some evaluation indexes, as modularity, this process can end at any point, and now the composition of this network is just thought several corporations.But the evaluation indexes such as modularity all exist defect, not yet there are generally acknowledged, a perfect evaluation index.The present invention not needs assessment index weighs the division to network, naturally network is divided into several corporations by the process of iteration.In general, after 3 to 5 iteration, the community structure of network will no longer change, and community structure now is just thought net result.
The present invention is applied to the centrality information of key node in the middle of community discovery.This thought is put forward by Yizhou Sun etc.Rankclus algorithm need to carry out initial division, and need to first specify corporations' number.Algorithm flow of the present invention does not need first to specify corporations' number, by the centrality information of key node is added in the middle of the calculating of the similarity between each node, obtain a similarity evaluation index-degree of membership, according to degree of membership, each node is condensed.
In the time that karate club network is divided, the NMI(normalized mutual information entropy between the division that discover method of the present invention obtains and true division) be 1, that is to say that the present invention can correctly divide nodes all in network.Node 10 is divided into " supervisor " corporations by CNM algorithm, and this is unique wrong node that is divided.As the degree of membership proposing by the present invention calculates, node 10 should belong to " principal " corporations.In the time that dolphin network is divided, CNM, BGLL algorithm are all some sub-corporations by large corporations' Further Division, because such division modularity is higher.Dolphin network can be divided into Liang Ge corporations, but the scale of one of them corporation is much larger than another corporations.Newman thinks that large corporations can further divide according to sex and age, uses GN algorithm really large corporations can be further divided into three Ge Zi corporations.The present invention is also divided into large corporations 3 Ge Zi corporations, therefore has higher NMI value.It is 1 result that MOGA-Net algorithm obtains also having in experimental result NMI.In the book network that Krebs provides, in fact should only have Liang Ge corporations, i.e. " freedom " and " guarding ", and the 3rd corporations are the books that cannot be distinguished its political orientation by those.Because the existence of the 3rd corporations causes the NMI of all algorithms not high.This network is divided into two large corporations by the present invention, and the books of " neutrality " are divided into respectively in the corporations of " freedom " and " guarding ", and this is closer to true division.In league football match network, there are some teams to oppose, do not belong to any alliance.Real network thinks that they are in same corporations in dividing, but the limit density of these corporations only has 0.1, and therefore, the present invention cannot mark off this class limit lower corporations of density from network.Except independent team, in " Sun Belt " corporations, node is also by wrong division, and this is mainly because the limit density of " Sun Belt " corporations is lower, only has 0.47.Node in other corporations can be correctly grouped together substantially.
Time complexity aspect, time complexity of the present invention is except outside the Pass having with the number n of nodes and the number m on limit, also relevant with the structure of network.In network, the scale of corporations is larger, and Riming time of algorithm is just more.This is that this all needs to calculate the triangle that two nodes can form because the calculating of algorithm of the present invention is mainly to ask the weight of limit and node.In the time programming, the coupled node of node is placed in same array.That is to say, the triangle of asking two nodes to form is equivalent to ask the common node of two arrays.In the time that in network, corporations are on a grand scale, each node probably has many connected nodes, and its corresponding array also can be very large, and the common node calculating between each array will be very consuming time.Therefore, be difficult to represent with a definite formula time complexity of algorithm of the present invention.For the network of general structure, the time complexity of algorithm of the present invention approaches linear, and the experimental result of table 1 shows, the present invention is significantly less than CNM algorithm the working time on large scale network.
Contrast working time on large scale network data set of table 1 the present invention and CNM algorithm
As shown in Table 1, the working time on data set roadNet_PA, roadNet_CA is identical with CNM all far fewer than CNM algorithm the working time on data set com-Amazon, com-DBLP and com-youtube in the present invention.For network sparse and level, the time complexity of CNM algorithm is O (nlog 2n), approached linearity.The scale of com-Amazon and com-DBLP is suitable, all have an appointment 300k node and 1M limit, but the two network structure difference causes differ greatly working time.Analyzed, in network, corporations' scale is larger before, and working time of the present invention is just longer.In com-Amazon, approximately there are 151k corporations, and Yue You13kGe corporations in com-DBLP.That is to say, in com-DBLP, the scale of corporations is greater than com-Amazon, so consuming time more.The scale of roadNet_PA, roadNet_CA is greater than com-Amazon and com-DBLP, but corporations are all very little, will lack so consuming time.The scale of roadNet_CA is approximately the twice of roadNet_PA, and the consuming time of the present invention and CNM algorithm is all also twice.RoadNet_PA, roadNet_CA are highway networks, comparatively sparse and have level significantly, so CNM less and linear growth consuming time.In com-youtube, there is 1M node, but 8k the corporations that only have an appointment, the scale of corporations is much larger than other networks, and therefore its is consuming time also far above other networks.But performance of the present invention is also much better than CNM algorithm, exceeded 4 hours the latter's working time.To sum up, for the small network of corporations, time complexity of the present invention approaches linear.
Embodiment, the present invention, in the time that the network in Fig. 3 is analyzed, first calculates the limit strength of joint of each connected node.For example, the limit strength of joint in Fig. 3 between node 1 and node 2 is 1, because a triangle of they compositions, and node 2 can not form triangle with node 4, the limit strength of joint between them is 0.Afterwards, enter the process of iteration, what Fig. 4 represented the is detailed step of iteration for the first time.In iteration for the first time, each node proceeds as follows according to number order: first under former, corporations, shift out, then calculate the degree of membership between each corporations, finally node division is arrived in the middle of the corporations of degree of membership maximum.Dotted line in Fig. 4 represents the corporations in network, and each node is as independent corporations at the beginning.Each step in Fig. 4 all can shift out the node of corresponding numbering, division operation.For example, the 3rd step is that node 3 is operated, and first it is shifted out from the corporations of own independent composition, now node 3 is for four corporations { (1,2), (4), (5), (6) degree of membership be respectively 4,0,0,0, so node 3 is divided in the middle of corporations (1,2).Because three nodes in corporations (1,2,3) can form a triangle, the key of these three nodes becomes 1.Carrying out iteration for the second time, the community structure at networking is identical with the structure of final step for the first time, and algorithm stops.

Claims (4)

1. the complex network community discover method based on topological property, is characterized in that, comprising:
Step 1, initialization; Using the each node in network as corporations independently, if there be n node in network, so just there are n initialization corporations, the key of each node is 0, degree of membership depends on limit strength of joint;
Step 2, calculates limit strength of joint; Calculate the limit strength of joint between all connected nodes, the leg-of-mutton number that two nodes that namely calculating has limit to be connected form;
Step 3, iteration; In order each node is carried out to following operation: first, a node is deleted from its place corporations, calculated the degree of membership of this node and each corporations, the corporations by node division to degree of membership maximum.
In step 3, after node is divided into new corporations, the center degree of coupled node may change, and need to recalculate the key of them, the leg-of-mutton number that can form; Afterwards, next node is carried out to same operation; When having traveled through all nodes, one time iteration finishes; Through iteration repeatedly, the ownership of each node will no longer change, and algorithm stops.
2. the complex network community discover method based on topological property as claimed in claim 1, is characterized in that, described limit strength of joint is for weighing two similarities between connected node, using s ijrepresent the limit strength of joint between node i and node j, s ijequal to comprise the leg-of-mutton number that node i and node j form in networking.
3. the complex network community discover method based on topological property as claimed in claim 1, is characterized in that, described key, is to weigh node significance level in corporations under it, uses c jrepresent node j key in corporations under it, c jequal in corporations, to comprise the leg-of-mutton number of node j under node j.
4. the complex network community discover method based on topological property as claimed in claim 1, is characterized in that, described degree of membership is the criterion of node division, i.e. relation between node and each corporations; Degree of membership computing formula is as follows:
A ( i , g ) = Σ j ∈ g ( ( 1 + s ij ) . ( 1 + c j r ) ) - - - ( 1 )
Wherein A (i, g) is with regard to the degree of membership of representation node i and the g of corporations, s ijthe limit strength of joint of node j in representation node i and the g of corporations, c jkey in the g of corporations of representation node j, r is coefficient, is preferably 10.
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