Researchers have devoted themselves to exploring static features of social networks and further discovered many representative characteristics, such as power law in the degree distribution and assortative value used to differentiate social networks from nonsocial ones. However, people are not satisfied with these achievements and more and more attention has been paid on how to uncover those dynamic characteristics of social networks, especially how to track community evolution effectively. With these interests, in the paper we firstly display some basic but dynamic features of social networks. Then on its basis, we propose a novel core-based algorithm of tracking community evolution, CommTracker, which depends on core nodes to establish the evolving relationships among communities at different snapshots. With the algorithm, we discover two unique phenomena in social networks and further propose two representative coefficients: GROWTH and METABOLISM by which we are also able to distinguish social networks from nonsocial ones from the dynamic aspect. At last, we have developed a social network model which has the capabilities of exhibiting two necessary features above.
A lot of work has been dedicated to exploring the characteristics of social networks. Barabasi and Albert show an uneven distribution of degree through BA models @cite_16 . Newman has successfully discovered distinct characteristics between social networks and nonsocial ones @cite_14 . Various methods have been utilized to detect community structures. Among them, there are Newman's betweenness algorithm @cite_12 @cite_10 , Nan Du's clique-based algorithm @cite_3 and CPM @cite_2 that focuses on finding overlapping communities. Clustering is another technique to group similar nodes into large communities, including L. Donetti and M.Miguel's method @cite_9 which exploits spectral properties of the graph as well as Laplacian matrix and J. Hopcroft's natural community'' approach @cite_17 . Some social network models have been proposed @cite_5 @cite_1 @cite_11 .
@cite_14 @cite_11 @cite_9 @cite_1 @cite_3 @cite_2 @cite_5 @cite_16 @cite_10 @cite_12 @cite_17
2103135182 1976160665 1992190284 2171608649
Based on Newman's fast algorithm [13], in this paper we develop a general probabilistic framework for detecting community structure in a network. The key idea of our generalization is to characterize a network (graph) by a bivariate distribution that specifies the probability of the two vertices appearing at both ends of a randomly selected path in the graph. With such a bivariate distribution, we give a probabilistic definition of a community and a definition of a modularity index. To detect communities in a network, we propose a class of distribution-based clustering algorithms that have comparable computational complexity to that of Newman's fast algorithm. Our generalization provides the additional freedom to choose a bivariate distribution and a correlation measure. As such, we obtain significant performance improvement over the original Newman fast algorithm in the computer simulations of random graphs with known community structure. Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks. This paper proposes a novel method based on fuzzy clustering to detect community structure in complex networks. In contrast to previous studies, our method does not focus on a graph model, but rather on a fuzzy relation model, which uses the operations of fuzzy relation to replace a traversal search of the graph for identifying community structure. In our method, we first use a fuzzy relation to describe the relation between vertices as well as the similarity in network topology to determine the membership grade of the relation. Then, we transform this fuzzy relation into a fuzzy equivalence relation. Finally, we map the non-overlapping communities as equivalence classes that satisfy a certain equivalence relation. Because most real-world networks are made of overlapping communities (e.g., in social networks, people may belong to multiple communities), we can consider the equivalence classes above as the skeletons of overlapping communities and extend our method by adding vertices to the skeletons to identify overlapping communities. We evaluated our method on artificial networks with built-in communities and real-world networks with known and unknown communities. The experimental results show that our method works well for detecting these communities and gives a new understanding of network division and community formation. We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow one to consider the best available two-way and three-way divisions at each recursive step. We illustrate the method using simple "bucket brigade" examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of U. S. Congressional networks inferred from roll call voting similarities.