On Proximity and Structural Role-based Embeddings in Networks

Abstract

Structural roles define sets of structurally similar nodes that are more similar to nodes inside the set than outside, whereas communities define sets of nodes with more connections inside the set than outside. Roles based on structural similarity and communities based on proximity are fundamentally different but important complementary notions. Recently, the notion of structural roles has become increasingly important and has gained a lot of attention due to the proliferation of work on learning representations (node/edge embeddings) from graphs that preserve the notion of roles. Unfortunately, recent work has sometimes confused the notion of structural roles and communities (based on proximity) leading to misleading or incorrect claims about the capabilities of network embedding methods. As such, this article seeks to clarify the misconceptions and key differences between structural roles and communities, and formalize the general mechanisms (e.g., random walks and feature diffusion) that give rise to community- or role-based structural embeddings. We theoretically prove that embedding methods based on these mechanisms result in either community- or role-based structural embeddings. These mechanisms are typically easy to identify and can help researchers quickly determine whether a method preserves community- or role-based embeddings. Furthermore, they also serve as a basis for developing new and improved methods for community- or role-based structural embeddings. Finally, we analyze and discuss applications and data characteristics where community- or role-based embeddings are most appropriate.