Comparison of Communities Detection Algorithms for Multiplex

Complexity Science studies the collective behaviour of a system of interacting agents, and a graph (network) is often an apt representation to visualize such systems. Traditionally the agents are expressed as the vertices, and an edge between a vertex pair implies that there are interactions between them. However the modern outlook in Network Science is to generalize the edges to encapsulate the multiple type of relationships between agents. For example in a social network, people are acquainted through work, school, family, etc. This is to preserve the richness of the data and to reveal deeper perspectives of the system. This is known as a multiplex. Multiplex is a natural transition from graphs and many disciplines independently studied this mathematical model for various applications like communities detection. A community refers to a set of vertices that behaves differently from the rest of the system. This is to modularize a complex system into simpler representations to form the bigger picture of the information flow. The first half of this paper is a literature review of the different communities detection algorithms and some theoretical bounds on graph cutting. Next we propose a suite of benchmark multiplexes and similarity metrics to determine the similarity of various communities detection algorithms. Finally we present the empirical results for this paper.