Tunable and Growing Network Generation Model with Community Structures

Recent years have seen a growing interest in the modeling and simulation of social networks to understand several social phenomena. Two important classes of networks, small world and scale free networks have gained a lot of research interest. Another important characteristic of social networks is the presence of community structures. Many social processes such as information diffusion and disease epidemics depend on the presence of community structures making it an important property for network generation models to be incorporated. In this paper, we present a tunable and growing network generation model with small world and scale free properties as well as the presence of community structures. The major contribution of this model is that the communities thus created satisfy three important structural properties: connectivity within each community follows power-law, communities have high clustering coefficient and hierarchical community structures are present in the networks generated using the proposed model. Furthermore, the model is highly robust and capable of producing networks with a number of different topological characteristics varying clustering coefficient and inter-cluster edges. Our simulation results show that the model produces small world and scale free networks along with the presence of communities depicting real world societies and social networks.Comment: Social Computing and Its Applications, SCA 13, Karlsruhe : Germany (2013

Small world networks and clustered small world networks with random connectivity

International audienceThe discovery of small world properties in real-world networks has revolutionized the way we analyze and study real-world systems. Mathematicians and physicists in particular have closely studied and developed several models to artificially generate networks with small world properties. The classical algorithms to produce these graphs artificially make use of the fact that with the introduction of some randomness in ordered graphs, small world graphs can be produced. In this paper, we present a novel algorithm to generate graphs with small world properties based on the idea that with the introduction of some order in a random graph, small world graphs can be generated. Our model starts with a randomly generated graph. We then replace each node of the random graph with cliques of different sizes. This ensures that the connectivity between the cliques is random but the clustering coefficient increases to a desired level. We further extend this model to incorporate the property of community structures (clusters) found readily in real-world networks such as social, biological and technological networks. These community structures are densely connected regions of nodes in a network that are loosely connected to each other. The model generates these clustered small world graphs by replacing nodes in the random graph with densely connected set of nodes. Experimentation shows that these two models generate small world and clustered small world graphs, respectively, as we were able to produce the desired properties of a small world network with high clustering coefficient and low average path lengths in both cases. Furthermore, we also calculated relative density and modularity to show that the clustered networks indeed had community structures

Identifying the Presence of Communities in Complex Networks Through Topological Decomposition and Component Densities

International audienceThe exponential growth of data in various fields such as Social Networks and Internet has stimulated lots of activity in the field of network analysis and data mining. Identifying Communities remains a fundamental technique to explore and organize these networks. Few metrics are widely used to discover the presence of communities in a network. We argue that these metrics do not truly reflect the presence of communities by presenting counter examples. This is because these metrics concentrate on local cohesiveness among nodes where the goal is to judge whether two nodes belong to the same community or vise versa. Thus loosing the overall perspective of the presence of communities in the entire network. In this paper, we propose a new metric to identify the presence of communities in real world networks. This metric is based on the topological decomposition of networks taking into account two important ingredients of real world networks, the degree distribution and the density of nodes. We show the effectiveness of the proposed metric by testing it on various real world data sets

Topological Decomposition and Heuristics for High Speed Clustering of Complex Networks

International audienceWith the exponential growth in the size of data and networks, development of new and fast techniques to analyze and explore these networks is becoming a necessity. Moreover the emergence of scale free and small world properties in real world networks has stimulated lots of activity in the field of network analysis and data mining. Clustering remains a fundamental technique to explore and organize these networks. A challenging problem is to find a clustering algorithm that works well in terms of clustering quality and is efficient in terms of time complexity. In this paper, we propose a fast clustering algorithm which combines some heuristics with a Topological Decomposition to obtain a clustering. The algorithm which we call Topological Decomposition and Heuristics for Clustering (TDHC) is highly efficient in terms of asymptotic time complexity as compared to other existing algorithms in the literature. We also introduce a number of Heuristics to complement the clustering algorithm which increases the speed of the clustering process maintaining the high quality of clustering. We show the effectiveness of the proposed clustering method on different real world data sets and compare its results with well known clustering algorithms

Evaluating the Quality of Clustering Algorithms using Cluster Path Lengths

International audienceMany real world systems can be modeled as networks or graphs. Clustering algorithms that help us to organize and understand these networks are usually referred to as, graph based clustering algo- rithms. Many algorithms exist in the literature for clustering network data. Evaluating the quality of these clustering algorithms is an impor- tant task addressed by different researchers. An important ingredient of evaluating these clustering techniques is the node-edge density of a clus- ter. In this paper, we argue that evaluation methods based on density are heavily biased to networks having dense components, such as social net- works, but are not well suited for data sets with other network topologies where the nodes are not densely connected. Example of such data sets are the transportation and Internet networks. We justify our hypothesis by presenting examples from real world data sets. We present a new metric to evaluate the quality of a clustering algorithm to overcome the limitations of existing cluster evaluation techniques. This new metric is based on the path length of the elements of a cluster and avoids judging the quality based on cluster density. We show the effectiveness of the proposed metric by comparing its results with other existing evaluation methods on artificially generated and real world data sets

Organization of Information for the Web using Hierarchical Fuzzy Clustering Algorithm based on Co-Occurrence Networks

International audienceIn this paper, we present a Hierarchical Fuzzy Clustering algorithm which uses domain knowledge to automatically determine the number of clusters and their initial values. The algorithm is applied on a collection of web pages and the results are compared with existing algorithms in the literature