Algorithm and Application for Signed Graphlets

Abstract

As the world is flooded with deluge of data, the demand for mining data to gain insights is increasing. One effective technique to deal with the problem is to model the data as networks (graphs) and then apply graph mining techniques to uncover useful patterns. Several graph mining techniques have been studied in the literature, and graphlet-based analysis is gaining popularity due to its power in exposing hidden structure and interaction within the networks. The concept of graphlets for basic (undirected) networks was introduced around 2004 by Pržulj, et. al. [14]. Subsequently, graphlet based network analysis gained attraction when Pržulj added the concept of graphlet orbits and applied to biological networks [15]. A decade later, Sarajlić, et. al. introduced graphlets and graphlet orbits for directed networks, illustrating its application to fields beyond biology such as world trade networks, brain networks, communication networks, etc. [19]. Hence, directed graphlets are found to be more powerful in exposing hidden structures of the network than undirected graphlets of same size, due to added information on the edges. Taking this approach further, more recently, graphlets and orbits for signed networks have been introduced by Dale [3]. This paper presents a simple algorithm to enumerate signed graphlets and orbits. It then demonstrates an application of signed graphlets and orbits to a metabolic network.