One of the most widely studied problem in mining and analysis of complex networks is the detection of community structures. The problem has been extensively studied by researchers due to its high utility and numerous applications in various domains. Many algorithmic solutions have been proposed for the community detection problem but the quest to find the best algorithm is still on. More often than not, researchers focus on developing fast and accurate algorithms that can be generically applied to networks from a variety of domains without taking into consideration the structural and topological variations in these networks. In this paper, we evaluate the performance of different clustering algorithms as a function of varying network topology. Along with the well known LFR model to generate benchmark networks with communities,we also propose a new model named Naive Scale Free Model to study the behavior of community detection algorithms with respect to different topological features. More specifically, we are interested in the size of networks, the size of community structures, the average connectivity of nodes and the ratio of inter-intra cluster edges. Results reveal several limitations of the current popular network clustering algorithms failing to correctly find communities. This suggests the need to revisit the design of current clustering algorithms that fail to incorporate varying topological features of different networks.
Lancichinetti and Fortunato @cite_27 also proposed methods to generate benchmarks for directed and weighted networks as well as networks with overlapping community structures but in this study, we limit our analysis to undirected, unweighed graphs with hard and flat community structures.
@cite_27
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Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogeneous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, such as social networks. As a practical application, we show how modularity optimization performs on our benchmark. Communities of vertices within a giant network such as the World-Wide Web are likely to be vastly smaller than the network itself. However, Fortunato and Barth ' e lemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than @math edges, where @math is the number of edges in the entire network. This resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks. Fortunato and Barth ' e lemy's argument can be extended to networks with weighted edges as well, and we derive this corollary argument. We conclude that weighted modularity algorithms may fail to resolve communities with fewer than @math total edge weight, where @math is the total edge weight in the network and @math is the maximum weight of an inter-community edge. If @math is small, then small communities can be resolved. Given a weighted or unweighted network, we describe how to derive new edge weights in order to achieve a low @math , we modify the CNM'' community detection algorithm to maximize weighted modularity, and show that the resulting algorithm has greatly improved accuracy. In experiments with an emerging community standard benchmark, we find that our simple CNM variant is competitive with the most accurate community detection methods yet proposed. Uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom [Proc. Natl. Acad. Sci. U.S.A. 104, 7327 (2007); Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008)], [J. Stat. Mech.: Theory Exp. (2008), P10008], and Ronhovde and Nussinov [Phys. Rev. E 80, 016109 (2009)] have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems. Uncovering the community structure exhibited by real networks is a crucial step towards an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom, and Ronhovde and Nussinov, respectively, have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.