In order to find the structure of local community more effectively, we propose an improved local community detection algorithm ILCDSP, which improves the node selection strategy, and sets selection probability value for every candidate node. ILCDSP assigns nodes with different selection probability values, which are equal to the degree of the nodes to be chosen. By this kind of strategy, the proposed algorithm can detect the local communities effectively, since it can ensure the best search direction and avoid the local optimal solution. Various experimental results on both synthetic and real networks demonstrate that the quality of the local communities detected by our algorithm is significantly superior to the state-of-the-art methods.
In the real world, many complex systems can be described through various kinds of networks, such as interpersonal networks, biological networks, neural networks, social networks, and WWW. Commonly, in these networks, individuals represented by nodes are linked with some special relationships. A large amount of studies reveal that there exist underlying communities in most complex networks. Community detection, as a key technology for network analysis, can discover the hidden structures and functions in complex networks, which is attracting a considerable amount of attention from researchers in various domains.
In recent years, a large number of community detection algorithms have been proposed, such as module optimization algorithm [
Some local community detection algorithms have been proposed based on the limited information, such as Clauset [
Problem of previous algorithms.
To solve the above problem, we propose an improved local community detection algorithm using selection probability (ILCDSP). The main idea of the algorithm is to set selection probability for the candidate nodes at each step, making the nodes with high selection probability more probably be chosen. ILCDSP screens nodes randomly; it does not just only select the node with high modularity, and thus it leads the algorithm process to the best search direction. It can avoid such a vicious circle that one misstep will undo all our work. The performance of the algorithm is verified, respectively, on the real and simulated data sets. The evaluation method used is Precision, Recall, and
The paper is organized as follows. Section
The definition of local community detection was firstly proposed by Clauset [
Definition of local community.
The task of local community detection is to constitute a local community
We have reviewed several effective approaches to explore local community structure. These algorithms are presented below in the sequence of publication date.
In order to solve the problem of local community detection, Clauset [
Local community modularity
The process of Clauset algorithm is similar to web crawler. First, it starts from a source node
The algorithm merges the neighbor nodes, which will be able to bring the biggest increment of
LWP [
Given an undirected graph
In the incremental step, the algorithm merges the nodes of
Bagrow and Bollt proposed a local community detection algorithm [
Most of the existing algorithms utilize the greedy strategy to select the present optimal node to join the local community. It can easily make the algorithm traps in local optimal solution. In order to avoid the occurrence of this phenomenon, this paper on the basis of the local community modularity, will give another selection criteria of nodes—selection probability.
LWP algorithm needs to select the subsequent node according to the largest increment of
The selection probability is determined by
ILCDSP algorithm generates random number
Steps of the algorithm are shown in Algorithm
(1) Merge the source node neighbor nodes of (2) Set local modularity (3) Calculate (4) (5) (6) Generate (7) Merge node (8) Update (9) (10)
ILCDSP algorithm firstly merges the source node
Here, we give an example to illustrate the application of the algorithm, as show in Figure
An example of application of ILCDSP.
The source node is the edge node
In order to improve the efficiency of the algorithm, for any node
The original calculation of
Firstly,
Compared to the original calculation of
This section verifies the performance of the improved algorithm ILCDSP. We will compare ILCDSP algorithm with several typical algorithms of local community detection; respectively, they are Clauset_
We select three real networks and LFR benchmark network as experimental data.
(1) LFR benchmark network [
Information of LFR benchmark network.
Num |
|
|
max |
min |
max |
|
---|---|---|---|---|---|---|
B1 | 1000 | 20 | 50 | 10 | 50 | 0.1~0.9 |
B2 | 1000 | 20 | 50 | 20 | 100 | 0.1~0.9 |
B3 | 5000 | 20 | 50 | 10 | 50 | 0.1~0.9 |
B4 | 5000 | 20 | 50 | 20 | 100 | 0.1 ~0.9 |
(2) The detailed information of real network data is shown in Table
Information of real networks.
Num | Name | Node number | Edge number | From |
---|---|---|---|---|
R1 | Karate | 34 | 78 | [ |
R2 | Football | 115 | 613 | [ |
R3 | Polbooks | 105 | 441 | [ |
We utilize
Figures
Comparison of B1.
Comparison of B2.
Comparison of B3.
Comparison of B4.
In our experiments, we apply each algorithm, respectively, in three real networks. Table
Comparison of different real networks.
Datasets | Evaluation | Clauset_ |
Clauset_ |
LWP | ILCDSP |
---|---|---|---|---|---|
Karate |
|
|
|
0.601 | 0.895 |
|
0.585 | 0.585 | 0.278 |
|
|
|
0.675 | 0.675 | 0.329 |
|
|
|
|||||
Football |
|
0.665 | 0.665 | 0.588 |
|
|
0.743 | 0.743 | 0.543 |
|
|
|
0.691 | 0.691 | 0.475 |
|
|
|
|||||
Polbooks |
|
|
|
0.651 | 0.760 |
|
0.478 | 0.478 | 0.183 |
|
|
|
0.520 | 0.520 | 0.217 |
|
Comparison of different real networks.
This paper proposed an improved local community detection algorithm—ILCDSP. The algorithm firstly sets selection probability for each candidate node, making the nodes with high selection probability more likely to be selected, and then it randomly screens nodes. The algorithm will process to the best direction, so as to improve the accuracy of local community detection. Experimental results show that ILCDSP could detect the structure of the local community more effectively than other algorithms both in the real and simulate networks.
Although this proposed algorithm improves the accuracy of community detection, it is not stable enough; at the same time, it remains to be further researched and improved in time.
The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work; there is no professional or other personal interest of any nature or kind in any product, service, or company that could be construed as influencing the position presented in or the review of the paper entitled.
This work was supported by the Fundamental Research Funds for the Central Universities, the National High Technology Research and Development Program of China (863 Program) (no. 2012AA011004 and no. 2012AA0622022), the Fundamental Research Funds for the Central Universities under Grant (no. 2013XK10), and the Doctoral Fund of the Ministry of Education (no. 20100095110003 and no. 20110095110010).