On structural entropy of uniform random intersection graphs

Recently, the need for efficient representations of data conveyed by graphical structures has emerged in many different contexts. While compressing such data one must consider two types of information. The first type is the information carried by the labels embedded in the structure. The second type is the information conveyed by the structure itself. In this extended abstract we address the latter type, namely we study the information carried by the structure of Uniform Random Intersection Graphs (URIGs). Random Intersection Graphs emerge in many scenarios, e.g., they correspond to the topology of many social networks and secure wireless networks, and they are induced in the clusterization process. We analyze algebraic properties of an automorphism group of the underlying structure of URIGs and derive a precise asymptotic formula for their structural entropy for various values of model parameters.