Cosine similarity for multiplex network summarization

Most of the natural systems encountered in all kinds of disciplines consist of a set of elementary units connected by relationships of different kinds. These complex systems are commonly described in terms of networks, where nodes represent the entities and links represent their interactions. As multiple types of distinct interactions are often observed, these systems are described as multiplex networks where the different types of interactions between the nodes constitute the different layers of the network. The ever-increasing size of these networks introduces new computational challenges and is therefore imperative to be able to eliminate the redundant or irrelevant edges of a network and create a summary that maintains the intrinsic properties of the original network, with respect to the overall structure of the system. In this work, we present a summarization technique for multiplex networks designed to maintain the structural characteristics of such complex systems by utilizing the intrinsic multiplex structure of the network and taking into consideration the inter-connectivity of the various graph layers. We validate our approach on real-world systems from different domains and show that our approach allows for the creation of more compact summaries, with minimum change of the structure evaluation measures, when compared to baseline methods that aggregate contributions of multiple types of interactions.