A large number of networks in nature, society and technology are defined by a mesoscopic level of organization, in which groups of nodes form tightly connected units, called communities, that are sparsely inter-linked to each other .Identifying this community structure is one of the most important problems in understanding of functions and structures of real world complex systems, which is still a challenging task. Various methods proposed so far are not efficient and accurate for large networks which comprise of millions of nodes because of their high computational cost.In this manuscript we will provide the implementation and behavioral analysis of BGLL algorithm for determining the structure of complex networks. This method is a variant of hierarchical agglomerative clustering approach, which finds the communities which are nested within one another. This method emphasizes on the idea of building the communities by combining the initial partition into super networks by repeatedly optimizing the modularity.In this work we will implement the BGLL Algorithm on various large networks which exhibit the community structure .We will also determine the optimal modularity at every pass and determine the hierarchical structure of large complex systems that comprise of millions of nodes. We will also provide a brief comparison of BGLL algorithm with some methods. General TermsGraph Theory, Data Mining.

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Cluster analysis of graph related problems is an important issue now-a-day. Different types of graph

There is an increasing interest in the research of clustering or finding communities in complex networks. Graph clustering and graph partitioning algorithms have been applied to this problem. Several graph clustering methods are come into the field but problem lies in the model espoused by the state-ofthe-art graph clustering algorithms for solving real-world situation. In this work, an attempt is made to provide an advanced cost based graph clustering algorithm based on stochastic local search. The proposed algorithm delivers significant improvement in robustness and quality of clustering in case of real-world complex network problems. The approach is to compute the cost (scaled cost) accurately when a target node is moved from source to destination cluster. The accurate cost is obtained by computing the induced effect which is evaluated by considering the relevance of nodes related to both source and destination clusters other than the target node during clustering. In our algorithm, moves are only made if the target node has neighbouring nodes in the destination cluster (moves to an empty cluster are the only exception to this instruction). Another important attachment in our approach is in inclusion of the aspiration criteria for the best move (lower-cost changes) selection when the best non-tabu move contributes much higher cost compared to a tabued move then the tabued move is acceptable otherwise the best non-tabu move is approved. Extensive experimentation with synthetic and real random geometric graph (RGG) benchmark datasets show that our algorithm outperforms state-of-the-art graph clustering techniques on the basis of cost of clustering, cluster size, normalized mutual information (NMI) and modularity index of clustering results.

The exploration of quality clusters in complex networks is an important issue in many disciplines, which still remains a challenging task. Many graph clustering algorithms came into the field in the recent past but they were not giving satisfactory performance on the basis of robustness, optimality, etc. So, it is most difficult task to decide which one is giving more beneficial clustering results compared to others in case of real-world problems. In this paper, performance of RNSC (Restricted Neighbourhood Search Clustering) and MCL (Markov Clustering) algorithms are evaluated on a random geometric graph (RGG). RNSC uses stochastic local search method for clustering of a graph. RNSC algorithm tries to achieve optimal cost clustering by assigning some cost functions to the set of clusterings of a graph. Another standard clustering algorithm MCL is based on stochastic flow simulation model. RGG has conventionally been associated with areas such as statistical physics and hypothesis testing but have achieved new relevance with the advent of wireless ad-hoc and sensor networks. In this study, the performance testing of these methods is conducted on the basis of cost of clustering, cluster size, modularity index of clustering results and normalized mutual information (NMI) using both real and synthetic RGG. General TermsGeneral Terms: Graph clustering, Data mining et. al.