CN116308860B - Dynamic community detection method based on allocation and splitting - Google Patents
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Abstract
The method detects the community structure of a first snapshot network by considering closeness among nodes, allocates communities for active nodes reflecting network changes and defines edge increasing nodes by considering the influence of new edges on community detection precision in a subsequent snapshot network, splits the allocated community structure into a plurality of local communities constructed by the edge increasing nodes and single communities constructed by other nodes, and optimizes the split communities by using modular gain combination, thereby detecting the final community structure. The method can detect a community structure with higher quality, and compared with other methods, the method reduces error accumulation of an increment method in the last snapshot of each real dynamic network, and obtains the highest Q value.
Description
Technical Field
The invention relates to the technical field of complex networks, in particular to a dynamic community detection method based on distribution and splitting.
Background
Community structure detection is a fundamental problem in complex network research of social, biological, traffic and the like. The community detection in the social network can mine trending topics of users for network public opinion control. Due to frequent interactions between nodes in a dynamic social network, different evolution behaviors have a certain influence on the community structure. Thus, researchers have proposed a number of dynamic community detection methods, among which widely used detection methods are classified into static detection methods, optimization-based detection methods, and delta-based detection methods.
In the static detection method, since community detection of different snapshot networks in the dynamic network is relatively independent, the community structure of valuable information contained in the previous snapshot network is ignored in the detection process. In order to consider the influence of the historical community structure, the community detection is converted into a single or multi-objective optimization problem based on an optimization detection method. While such methods take into account the impact of historical community information, iterative optimization targets are a time-consuming process. The incremental-based method only needs to consider the changed nodes and edges in the network, so that the community detection efficiency in the dynamic network is greatly improved, and the smoothness of community evolution is ensured. However, as the network evolves, the error history information is accumulated, so the accuracy of the incremental community detection result is gradually reduced.
Disclosure of Invention
The invention provides a dynamic community detection method based on allocation and splitting, which aims to solve the problem that the existing dynamic community detection method based on increment is easily subjected to error accumulation due to the influence of an initial network community and an increment detection process.
A dynamic community detection method based on allocation and splitting is realized by the following steps:
step one, setting a network sequence G= { G for a dynamic network 0 ,G 1 ,…,G t ,…,G T ]A representation; wherein G is t ＝(V t ,E t ) For a snapshot network at time T, t=0, 1, …, T;
V t ＝{u t i u=1, 2, …, n } is snapshot network G t A set of n nodes;
for snapshot network G t A set of m sides of said +.>For slave node u t To node vt A kind of electronic device Edges>
CS＝{CS 0 ,CS 1 ,…,CS t ,…,CS T Is the community structure of the network sequence G, wherein For snapshot network G t Is a group of k communities;
step two, realizing a snapshot network G by adopting a static community division method based on public neighbor clustering entropy node similarity 0 Obtaining community structure CS by automatic community detection of (a) 0 In CS t-1 Is removed from G t-1 To G t Disappeared node and take it as G t Initial community structure of (a)
Step three, determining the movable node set
For each node u t Connecting communitiesA node with a difference between the inner and outer edges of greater than zero is called an active node +.>And constructs the active node set as +.>
Step four, identifying G t Active node set in (a)Active node set->Each active node of (a)>From->Removing and assigning communities to the same to obtain community structure +.>
Step five, the community structure obtained in the step fourMerging and optimizing to obtain a first-stage community structure
Step six, determining an edge-increasing node set
For each node u t-1 ∈V t-1 If node u t-1 From G t-1 To G t Change, node u t Then called change node, V C ＝{u t |d(u t-1 )≠d(u t ) And d (u) t-1 ) And d (u) t ) Respectively, are node u t-1 And u t A degree value of (2);
setting edgeFor new edge, node u t And node v t Belonging to the change node set V C And Community->Node u t Then called edge node ++>The edge-increasing node set is +.>Expressed by the following formula:
in the method, in the process of the invention,to from G t-1 To G t Is a new edge of (a);
step seven, determining local communities
When edge node is increasedAt the time, add edge node +.>Is the same as the edge node set +.>Is combined to form a local community, and an edge node is defined +.>The local community at time t isExpressed by the following formula:
in the method, in the process of the invention,is added with edge nodes->Is a neighbor node set;
step eight, determining a single instance community C t _Sig(u t )；
For communitiesNode->Then it is node u t Creating a single community, said single instance community C t _Sig(u t ) The method comprises the following steps:
step nine, local communities obtained according to step sevenAnd step eight, obtaining a single instance community C t _Sig(u t ) The community structure of the first stage is +.>The communities in the network are split, recombined and optimized to obtain a final community structure CS t 。
The invention has the beneficial effects that:
in the method, the community structure of a first snapshot network is detected by considering the closeness among nodes, communities are allocated for active nodes reflecting network changes in a subsequent snapshot network, edge-added nodes are defined by considering the influence of new edges on community detection precision, the allocated community structure is divided into a plurality of local communities constructed by the edge-added nodes and single communities constructed by other nodes, and the divided communities are combined and optimized by using modular gain, so that the final community structure is detected.
Comparing the evaluation indexes NMI and Q values obtained by the dynamic community detection method based on allocation and splitting and other community detection methods, it can be seen that the method can detect a community structure with higher quality along with the increase of the number of community merging and splitting events in the artificial synthesis dynamic network, and compared with other methods, the method reduces the error accumulation of an increment method and obtains the highest Q value in the last snapshot of each real dynamic network.
Drawings
FIG. 1 is a schematic diagram illustrating steps of a dynamic community detection method based on allocation and splitting according to the present invention.
Fig. 2 is a schematic diagram of an active node according to the present invention.
FIG. 3 is a schematic diagram of a community structure in an adjacent snapshot network according to the present invention.
Fig. 4 is a graph showing NMI and Q values versus algorithms in an LFR500 network with different merge and split events according to the present invention. Wherein: (a) NMI effect graphs of merge=3 and split=3 in a community structure merging and splitting evolution event; (b) NMI effect graphs of merge=5 and split=5 in a community structure merging and splitting evolution event; (c) NMI effect graphs of merge=10 and split=10 in a community structure merging and splitting evolution event; (d) A Q value effect graph with merge=3 and split=3 in a community structure merging and splitting evolution event; (e) A Q value effect graph with merge=5 and split=5 in a community structure merging and splitting evolution event; (f) A Q value effect graph with merge=10 and split=10 in a community structure merging and splitting evolution event;
fig. 5 is a graph showing NMI and Q values versus algorithms in an LFR1000 network with different merge and split events according to the present invention. Wherein: (a) NMI effect graphs of merge=5 and split=5 in a community structure merging and splitting evolution event; (b) NMI effect graphs of merge=10 and split=10 in a community structure merging and splitting evolution event; (c) NMI effect graphs of merge=20 and split=20 in a community structure merging and splitting evolution event; (d) A Q value effect graph with merge=5 and split=5 in a community structure merging and splitting evolution event; (e) A Q value effect graph with merge=10 and split=10 in a community structure merging and splitting evolution event; (f) A Q value effect graph with merge=20 and split=20 in a community structure merging and splitting evolution event;
fig. 6 is a schematic diagram showing the Q value comparison of different algorithms in a real dynamic network according to the present invention. The method comprises the steps of (a) comparing the Q value of the community structure detected by the ASCDA method with that of the community structure detected by the existing method by adopting an Office contact network; (b) The Q value comparison diagram of the community structure detected by the ASCDA method and the existing method is carried out by adopting the Enron email; (c) Adopting High school to carry out Q value comparison schematic diagram of the community structure detected by the ASCDA method and the existing method; (d) The Q value comparison diagram of the community structure detected by the ASCDA method and the existing method is carried out by adopting Primary school;
FIG. 7 is a graph showing average modularity of different algorithms in a real dynamic network.
Detailed Description
Detailed description of the inventionin the first embodiment, the dynamic community detection method based on allocation and splitting will be described with reference to fig. 1 to 3, and the specific steps are as follows:
step one, setting a network sequence G= { G for a dynamic network 0 ,G 1 ,…,G t ,…,G T -a }; wherein G is t ＝(V t ,E t ) For a snapshot network at time T (t=0, 1, …, T), V t ＝{u t Sum of |u=1, 2, …, n }, and for snapshot network G t A set of n nodes and m edges, here +.>Is slave node u t To node v t Of (1), wherein-> Is a community structure of the network G, wherein +.>For snapshot network G t Is a group of k communities;
snapshot network G t-1 To snapshot network G t Incremental change (i.e. G) t ＝G t-1 u.DELTA.G) is denoted as DELTA.G t ＝(ΔV t ,ΔE t ) Wherein DeltaV t And delta E t Respectively at time (t-1, t]A collection of nodes and edges that are changed inside. Thus, from G t The process of dividing communities in the middle may be expressed as (CS t-1 ,G t ,ΔG t )→CS t Dividing communities using incremental methods requires knowledge of the first snapshot network G of the dynamic network G 0 And incremental changes to neighboring snapshot networks.
Step two, realizing a snapshot network G by adopting a static community division method (CSCDA) based on public neighbor clustering entropy node similarity 0 Obtaining community structure CS by automatic community detection of (a) 0 In CS t-1 Is removed from G t-1 To G t Disappeared node and take it as G t Initial community structure of (a)
Step three, defining movable node set
Incremental changes of the snapshot network are represented by deletion and addition of nodes and edges, and the series of changes are represented by increase and decrease of node degree values;
for each node u t ∈V t Connecting communitiesA node with a difference between the inner and outer edges of greater than zero is called an active node +.>Define the active node set as +.>
In the method, in the process of the invention, is to combine node u t Connect to community->The number of edges beyond->Is node u t Is located in community->The number of edges inside; as shown in fig. 2, node u t-1 The degree value from time t-1 to time t is changed, the initial community structure at time t is +.>In node u t Connect community->The difference between the inner and outer edges of (2) is 1, so that node u t Becomes an active node at the time t, and the node is added with the community +.>The external connection needs to be considered again for communities to which the nodes belong;
step four, identifying G t Active node set in (a)In which each active node is selected from +.>Removing and assigning communities to them;
cosine similarity (Salton index) is proposed based on the structural relation of local neighborhood of nodes, and is suitable for local community division of a complex network. For active node setsEach of the movable nodes is arranged in descending order of illuminance value, and Salton index is adopted to be +.>Active node->Finding its similar neighbor nodes.
When similar neighbor nodes already belong to the communityWhen the node is active->Is assigned to communityOtherwise, the active node is->Merging neighboring nodes similar to the neighboring nodes to create a new community; if the similar neighbor nodes are also +>The node in (2) is no longer considered as active node +.>Distributing communities;
after all the movable nodes are distributed, a community structure is obtainedIncluding many sparse, dual-node communities, among others. The existence of a small community can reduce community quality, and has no meaning on the community structure of the network;
step five, according to the community structure obtained in the step fourCarrying out merging optimization to obtain a first-stage community structure +.>The method comprises the following steps:
fifthly, according to the module degree gain delta Q ij Is defined by:
in the formula e ij Is C i And C j The ratio of the number of continuous edges between (i.noteq.j) to the total number of edges; a, a i Is C with i The nodes in (a) being connected but the other node not belonging to C i The ratio of the number of edges to the total number of edges of the network; a, a j Is in combination withThe nodes of which are connected but the other node does not belong to +.>The ratio of the number of edges to the total number of edges of the network; k (k) i Is C i Of intermediate nodesSum of degrees; m is the total number of edges in the network;
step five, calculatingThe modularity gain between each pair of adjacent communities is selected, and two communities with the maximum modularity gain are selected>They are combined to form a new community.
Step five, repeating the step five two until the modularity gain is negative, and obtaining the community structure of the first stage
For incremental changes within the same community, the community affiliation of the node cannot fully reflect the changes within the community, but at node u belonging to the same community t-1 And v t-1 An edge is added between the two nodes, and the node u cannot be connected t And v t Partitioning into different communities, thus consider node u t And v t Separating the material from the community to further improve the quality of the community structure;
step six, defining an edge node set
For each node u t-1 ∈V t-1 If node u t-1 From G t-1 To G t Change, node u t Then called change node, V C ＝{u t |d(u t-1 )≠d(u t ) And d (u) t-1 ) And d (u) t ) Respectively, are node u t-1 And u t A degree value of (2);
edge(s)Is a new edge, node u t And v t Belonging to the change node set V C And->Node u t Then called edge node ++>Define the increased side node set as +.>
In the method, in the process of the invention,the representation is from G t-1 To G t Is a new edge of (a);
step seven, defining local communities
For edge nodeNode->Same as it pertains to->Is merged to form a local community, defining node +.>The local community at time t is +.>
In the method, in the process of the invention,for node->Is a neighbor node set;
step eight, defining a single instance community C t _Sig(u t )；
For communitiesNode->For node u t Creating a single community, defining a single instance community C t _Sig(u t ) The method comprises the following steps:
step nine, local communities obtained according to step sevenAnd step eight, obtaining a single instance community C t _Sig(u t ) Will->The communities in the network are split, combined and optimized to obtain a final community structure CS t The method specifically comprises the following steps:
step nine one, forEvery community->If node->For the edge node, access node u t Neighbor node set->Node u t Is associated with->Is combined with neighbor nodes to construct local communitiesOtherwise, it is node u t Creating a single instance community C t _Sig(u t ) The method comprises the steps of carrying out a first treatment on the surface of the When community-> If the node in the local community exists in a certain local community, a new local community is not created for the node in the local community; obtaining split community structure
The community at time t as shown in FIG. 3An edge is newly added between the middle node 5 and the node 6, namely the node 5 and the node 6 are edge adding nodes, and the node is +.>Node 5 and node 6 in (a) are combined to construct a local community +.>The remaining nodes construct a single instance community such as: c (C) t _Sig(1 t )＝{1}、C t _Sig(2 t )＝{2}、C t _Sig(3 t )＝{3}、C t _Sig(4 t )＝{4}；
Step nine, calculating according to the modularity gain of step fiveThe modularity gain between each pair of adjacent communities is selected, and two communities with the maximum modularity gain are selected>They are combined to form a new community.
For community structureEvery community->Executing the step nine and calculating the modularity of the corresponding community structure, and updating the ++according to the rule of increasing the modularity>Obtaining a final community structure CS t The method comprises the steps of carrying out a first treatment on the surface of the The final community structure CS as shown in FIG. 3 t = {1,2,4}, {3,5,6}, {7,8,9,10}, change from two communities at time t-1 to 3 communities, and change modularity from 0.35 at time t-1 to 0.38 at time t;
a second embodiment is described with reference to fig. 4 to fig. 7, where the second embodiment is an application example of the dynamic community detection method based on allocation and splitting described in the first embodiment.
Four real dynamic social networks of a synthetic dynamic network and Office contact network (Office contact), a middle school student interaction network (High school) and a Primary school student interaction network (Primary email) generated by an extended LFR model are selected, community detection is carried out on the four real dynamic social networks by using SCAN, QCA, inBatch and an incNSA method, corresponding evaluation indexes NMI and Q values are calculated, and NMI and Q values based on an allocation and splitting dynamic community detection method (Dynamic Community Detection Algorithm based on Allocating and Splitting, ASCDA for short) are compared.
The synthetic dynamic network is controlled by several parameters, such as node number, average degree, maximum degree, mixing parameters, snapshot number, and merge and split representing the merging and splitting evolution events of the community structure. In this embodiment, two scale synthetic dynamic networks were generated, and specific parameter settings of the LFR synthetic dynamic network are shown in table 1.
TABLE 1
| Network system | Node count | Average degree of | Maximum degree of | merge | split | Mixing parameters | Snapshot number |
| LFR500 | 500 | 10 | 30 | 3 | 3 | 0.2 | 10 |
| LFR500 | 500 | 10 | 30 | 5 | 5 | 0.2 | 10 |
| LFR500 | 500 | 10 | 30 | 10 | 10 | 0.2 | 10 |
| LFR1000 | 1000 | 20 | 40 | 5 | 5 | 0.2 | 10 |
| LFR1000 | 1000 | 20 | 40 | 10 | 10 | 0.2 | 10 |
| LFR1000 | 1000 | 20 | 40 | 20 | 20 | 0.2 | 10 |
Fig. 4 illustrates NMI and Q values for different methods with different merge and split events on LFR500 network, such as: fig. 4 (a), (b), (c), and fig. 4 (d), (e), (f), where the number of merging and splitting events is 3,5, and 10, respectively.
The NMI value of the ASCDA method is not optimal on the first snapshot network of each group of networks. The reason is that ASCDA employs a modularity optimization approach to achieve the final result. For a network with a real community structure, the community structure corresponding to the highest modularity is not necessarily the structure closest to the real community, so NMI value may be reduced. For subsequent snapshot networks, the ASCDA achieves optimal results on the remaining groups of networks of LFR500, except for the 2 nd and 5 th snapshots of FIGS. 4 (a) and (d). Compared to NMI values representing suboptimal IncNSA, NMI values of ASCDA over three groups of networks, namely: the improvement of the diagrams (a), (b) and (c) is 0.50%, 1.38% and 3.07%, respectively.
As can be seen in fig. 4 (d), the Q value of ASCDA is comparable to that of IncNSA on LFR500 network. On the LFR500 network in (e), the Q value of ASCDA is significantly raised over the last 3 snapshots. Compared with the IncNSA method, the Q value is improved by 1.72% on the LFR500 network in (f) most significantly. QCA and InBatch are both incremental detection methods, their performance gradually decreases over time, and the final NMI and Q values are both near 0.2. As can be seen from fig. 4 (f), the SCAN overall has a decreasing trend and has a large fluctuation.
As shown in fig. 5, in the LFR1000 network, the optimum values of NMI and Q of ASCDA in (a) and (d) are obtained in the LFR1000 network. The results of the SCAN, QCA and InBatch methods all show a decreasing trend. As the number of community merging and splitting events increases, the NMI and Q values of ASCDA in (b) and (e) are increased by 0.36% and 0.89% respectively over the IncNSA method. ASCDA has significant advantages when the number of community merge and split events reaches 20. Compared with the IncNSA method, the NMI and Q values of the ASCDA are respectively improved by 7.38 percent and 8.27 percent. Complex evolution behavior of community merging and splitting due to merge=20 and split=20: as in (c) and (f), the NMI and Q values of the ASCDA, SCAN and IncNSA methods fluctuate widely. In addition, the SCAN method is not excellent in (f) of fig. 5, and the difference between the maximum Q value and the minimum Q value is close to 0.8. This is because the conventional method independently detects each snapshot, and ignores the evolution behavior of the community.
By combining the NMI and Q metrics, the performance of the ASCDA method is more outstanding along with the increase of the number of community merging and splitting events.
Table 2 gives the basic information of 4 real dynamic networks.
TABLE 2
| Network system | Snapshot number | Maximum node number | Minimum node number | Maximum edge number | Minimum edge number |
| Office contact | 10 | 72 | 59 | 188 | 94 |
| High school | 9 | 159 | 16 | 747 | 11 |
| Primary school | 18 | 236 | 117 | 2137 | 628 |
| Enron email | 44 | 18396 | 19 | 48471 | 19 |
As the real dynamic network does not have a real community structure, the modularity Q is used to compare the comparison results of the method of the invention with other dynamic community detection methods on Office contact, high school, primary school and Enron email networks as shown in FIG. 6.
The Q value of the community structure detected by the ASCDA method in the Office contact network shown in fig. 6 (a) is similar to that of the IncNSA method, but is still 0.73% higher than that of the IncNSA method. The SCAN method has large fluctuation of Q value, while QCA and InBatch methods are relatively stable, and the Q value is concentrated at about 0.4.
The Enron Email network collected data from month 11 1998 to month 6 2002, and no obvious community structure was formed due to less communication between Email contacts from month 11 1998 to month 2 1999. The ASCDA method still yields a higher modularity Q value as shown in fig. 6 (b), where Q value reaches 0.54 on the 4 th snapshot network. In other snapshot networks, the Q values obtained by the ASCDA method are ranked first.
The 6 th snapshot network of the High school network counts the communication situation between Saturday students. Since this day is not a workday, there is less and relatively decentralised contact between students. Therefore, for this case, the ASCDA method shown in fig. 6 (c) has a Q value up to 32.26% higher than the IncNSA method.
As shown in fig. 6 (d), Q values of community structures reach the lowest point in the 4 th to 5 th snapshot networks of the Primary school network. At this time, the student may have more interactions with students in different classes during the dining time. Therefore, the community structure in the class becomes decentralized, resulting in a decrease in Q value. After noon break, the community structure changes again with the restoration of classroom learning activities. It can be seen that the ASCDA method has detected a community structure Q value of 0.8 after the community splitting and merging events are experienced. Compared with the IncNSA method, the Q value of the ASCDA is improved by 4.34 percent.
On the last snapshot of each real dynamic network, the ASCDA method achieves the highest Q value compared to other methods, indicating that it reduces the error accumulation of the incremental method. With the evolution of the network, the ASCDA can partition a corresponding high-quality community structure. The Q value of the last snapshot on the Office contact network and the High school network is even the highest Q value in the overall network evolution process.
As shown in fig. 7, the average modularity value of the ASCDA and IncNSA calculation method is always in the lead compared to other methods. In contrast, the SCAN method is not stable enough, ranks 3 rd in the Office contact network and the Primary school network, and ranks last in the High school and the acron Email networks. As the network scale increases, the gap between QCA and InBatch approaches increases. Given the large number of merge and split events between student interconnections, the ASCDA method has a significant improvement in average modularity over two student communication networks. Furthermore, the ASCDA method still works well on Office contact networks and acron email networks without obvious merge and split events.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (3)
1. A dynamic community detection method based on allocation and splitting is realized by the following steps:
step one, setting a network sequence G= { G for a dynamic network 0 ,G 1 ,…,G t ,…,G T -representation; wherein G is t ＝(V t ,E t ) For a snapshot network at time T, t=0, 1, …, T;
V t ＝{u t i u=1, 2, …, n } is snapshot network G t A set of n nodes;
for snapshot network G t A set of m sides of said +.>For slave node u t To node v t Of (1), wherein->
CS＝{CS 0 ,CS 1 ,…,CS t ,…,CS T Is the community structure of the network sequence G, wherein For snapshot network G t Is a group of k communities;
step two, realizing a snapshot network G by adopting a static community division method based on public neighbor clustering entropy node similarity 0 Obtaining community structure CS by automatic community detection of (a) 0 In CS t-1 Is removed from G t-1 To G t Disappeared node and take it as G t Initial community structure of (a)
Step three, determining the movable node set
For each node u t Connecting communitiesNodes with differences between the inner and outer edges greater than zero are referred to as active nodesAnd constructs the active node set as +.>
Step four, identifying G t Active node set in (a)Active node set->Each active node of (a)>From the slaveRemoving and assigning communities to the same to obtain community structure +.>
The specific process is as follows:
for movable node setEach movable node in the network is arranged in descending order of illumination value and adopts Salton indexes as follows in turnActive node->Find its similar neighbor node when it already belongs to the community +.>When the node is active->Assigned to community->Otherwise, the active node is->Merging neighboring nodes similar to the neighboring nodes to create a new community; if the similar neighbor nodes are also +>The node in (2) is no longer the active node +.>Assigning communities, and finally obtaining assigned community structures>
Step five, the community structure obtained in the step fourPerforming merging optimization to obtain a first-stage community structure +.>The specific process is as follows:
fifthly, according to the module degree gain delta Q ij Calculating the community structureModularity gain between each pair of adjacent communities;
step five, selecting two communities with the maximum modularity gain-putting the two communities->Merging to form a new community;
step five, repeating the step five two until the modularity gain is negative, and obtaining the community structure of the first stage
Step six, determining an edge-increasing node set
For each node u t-1 ∈V t-1 If node u t-1 From G t-1 To G t Change, node u t Then called change node, V C ＝{u t |d(u t-1 )≠d(u t ) And d (u) t-1 ) And d (u) t ) Respectively, are node u t-1 And u t A degree value of (2);
setting edgeFor new edge, node u t And node v t Belonging to the change node set V C And Community->Node u t Then called edge node ++>The edge-increasing node set is +.>Expressed by the following formula:
in the method, in the process of the invention,to from G t-1 To G t Is a new edge of (a);
step seven, confirmLocal community determination
When edge node is increasedAt the time, add edge node +.>Is the same as the edge node set +.>Is combined to form a local community, and an edge node is defined +.>The local community at time t is +.>Expressed by the following formula:
in the method, in the process of the invention,is added with edge nodes->Is a neighbor node set;
step eight, determining a single instance community C t _Sig(u t )；
For communitiesNode->Then it is node u t Creating a single community, said single instance community C t _Sig(u t ) The method comprises the following steps:
step nine, local communities obtained according to step sevenAnd step eight, obtaining a single instance community C t _Sig(u t ) The community structure of the first stage is +.>The communities in the network are split, recombined and optimized to obtain a final community structure CS t The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
step nine one, forEvery community->If node->For the edge node, access node u t Neighbor node set->Node u t Is associated with->Is combined with neighbor nodes to construct local communitiesOtherwise, it is node u t Creating a single instance community C t _Sig(u t ) The method comprises the steps of carrying out a first treatment on the surface of the If the community is-> If the node in the local community exists in a certain local community, a new local community is not created for the node; obtaining split Community Structure->
Step nine two, according to the module degree gain delta Q ij Calculation ofThe modularity gain between each pair of adjacent communities is selected, and two communities with the maximum modularity gain are selected>Combining them to form a new community;
sequentially accessing community structure of each first stageEvery community->And updating with the rule of module incrementObtaining a final community structure CS t 。
2. The dynamic community detection method based on allocation and splitting as claimed in claim 1, whereinThe method comprises the following steps: in the third step, the active node set isExpressed by the following formula:
in the method, in the process of the invention,to node u t Connect to community->The number of edges beyond->For node u t Is located in community->Number of sides in the interior.
3. The allocation and splitting-based dynamic community detection method of claim 1, wherein: in the fifth step, the module gain Δq ij Expressed by the following formula:
ΔQ ij ＝2(e ij -a i a j ),
in the formula e ij Is thatAnd->Connection betweenThe proportion of the number of edges to the total number of edges; a, a i Is->The nodes of which are connected but the other node does not belong to +.>The ratio of the number of edges to the total number of edges of the network; a, a j Is->The nodes of which are connected but the other node does not belong to +.>The ratio of the number of edges to the total number of edges of the network; k (k) i Is->The sum of the degrees of the middle nodes; m is the total number of edges in the network.
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