Structural Graph Representations based on Multiscale Local Network Topologies

Abstract

In many applications, it is required to analyze a graph merely based on its topology. In these cases, nodes can only be distinguished based on their structural neighborhoods and it is common that nodes having the same functionality or role yield similar neighbor-hood structures. In this work, we investigate two problems: (1) how to create structural node embeddings which describe a node’s role and (2) how important the nodes’ roles are for characterizing entire graphs. To describe the role of a node, we explore the structure within the local neighborhood (or multiple local neighborhoods of various extents) of the node in the vertex domain, compute the visiting probability distribution of nodes in the local neighborhoods and summarize each distribution to a single number by computing its entropy. Furthermore, we argue that the roles of nodes are important to characterize the entire graph. Therefore, we propose to aggregate the role representations to describe whole graphs for graph classification tasks. Our experiments show that our new role descriptors outperform state-of-the-art structural node representations that are usually more expensive to compute. Additionally, we achieve promising results compared to advanced state-of-the-art approaches for graph classification on various benchmark datasets often outperforming these approaches.