Network Community Detection on Metric Space

Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings

COMMUNITY DETECTION AND INFLUENCE MAXIMIZATION IN ONLINE SOCIAL NETWORKS

The detecting and clustering of data and users into communities on the social web are important and complex issues in order to develop smart marketing models in changing and evolving social ecosystems. These marketing models are created by individual decision to purchase a product and are influenced by friends and acquaintances. This leads to novel marketing models, which view users as members of online social network communities, rather than the traditional view of marketing to individuals. This thesis starts by examining models that detect communities in online social networks. Then an enhanced approach to detect community which clusters similar nodes together is suggested. Social relationships play an important role in determining user behavior. For example, a user might purchase a product that his/her friend recently bought. Such a phenomenon is called social influence and is used to study how far the action of one user can affect the behaviors of others. Then an original metric used to compute the influential power of social network users based on logs of common actions in order to infer a probabilistic influence propagation model. Finally, a combined community detection algorithm and suggested influence propagation approach reveals a new influence maximization model by identifying and using the most influential users within their communities. In doing so, we employed a fuzzy logic based technique to determine the key users who drive this influence in their communities and diffuse a certain behavior. This original approach contrasts with previous influence propagation models, which did not use similarity opportunities among members of communities to maximize influence propagation. The performance results show that the model activates a higher number of overall nodes in contemporary social networks, starting from a smaller set of key users, as compared to existing landmark approaches which influence fewer nodes, yet employ a larger set of key users

Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure

Application Oriented Analysis of Large Scale Datasets

Diverse application areas, such as social network, epidemiology, and software engineering consist of systems of objects and their relationships. Such systems are generally modeled as graphs. Graphs consist of vertices that represent the objects, and edges that represent the relationships between them. These systems are data intensive and it is important to correctly analyze the data to obtain meaningful information. Combinatorial metrics can provide useful insights for analyzing these systems. In this thesis, we use the graph based metrics such as betweenness centrality, clustering coefficient, articulation points, etc. for analyzing instances of large change in evolving networks (Software Engineering), and identifying points of similarity (Gene Expression Data). Computations of combinatorial properties are expensive and most real world networks are not static. As the network evolves these properties have to be recomputed. In the last part of thesis, we develop a fast algorithm that avoids redundant recomputations of communities in dynamic networks