Community detection has become an extremely active area of research in recent years, with researchers proposing various new metrics and algorithms to address the problem. Recently, the Weighted Community Clustering (WCC) metric was proposed as a novel way to judge the quality of a community partitioning based on the distribution of triangles in the graph, and was demonstrated to yield superior results over other commonly used metrics like modularity. The same authors later presented a parallel algorithm for optimizing WCC on large graphs. In this paper, we propose a new distributed, vertex-centric algorithm for community detection using the WCC metric. Results are presented that demonstrate the algorithm's performance and scalability on up to 32 worker machines and real graphs of up to 1.8 billion vertices. The algorithm scales best with the largest graphs, and to our knowledge, it is the first distributed algorithm for optimizing the WCC metric.
There also exist several proposals based on random walks. The intuition is that in a random walk, the probability of remaining inside of a community is higher than going outside, due to the higher density of internal edges. This strategy is the main idea exploited in Walktrap @cite_15 . Another algorithm based on random walks that is highly adopted in the literature is Infomap @cite_20 , which searches for a codification for describing random walks based on communities. The codification that requires the least amount of memory (attains the highest compression rates) is selected. According to the comparison performed by @cite_24 , Infomap stands as one of the best community detection algorithms in the literature.
@cite_24 @cite_15 @cite_20
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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. In a representative embodiment of the invention described herein, a well logging system for investigating subsurface formations is controlled by a general purpose computer programmed for real-time operation. The system is cooperatively arranged to provide for all aspects of a well logging operation, such as data acquisition and processing, tool control, information or data storage, and data presentation as a well logging tool is moved through a wellbore. The computer controlling the system is programmed to provide for data acquisition and tool control commands in direct response to asynchronous real-time external events. Such real-time external events may occur, for example, as a result of movement of the logging tool over a selected depth interval, or in response to requests or commands directed to the system by the well logging engineer by means of keyboard input. To comprehend the multipartite organization of large-scale biological and social systems, we introduce an information theoretic approach that reveals community structure in weighted and directed networks. We use the probability flow of random walks on a network as a proxy for information flows in the real system and decompose the network into modules by compressing a description of the probability flow. The result is a map that both simplifies and highlights the regularities in the structure and their relationships. We illustrate the method by making a map of scientific communication as captured in the citation patterns of >6,000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network—including physics, chemistry, molecular biology, and medicine—information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences.