Vertex nomination via seeded graph matching

Abstract

Consider two networks on overlapping, nonidentical vertex sets. Given vertices of interest (VOIs) in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching methods can be applied directly to recover the missing correspondences, herein we present a principled methodology appropriate for situations in which the networks are too large/noisy for brute-force graph matching. Our methodology identifies vertices in a local neighborhood of the VOIs in the first network that have verifiable corresponding vertices in the second network. Leveraging these known correspondences, referred to as seeds, we match the induced subgraphs in each network generated by the neighborhoods of these verified seeds, and rank the vertices of the second network in terms of the most likely matches to the original VOIs. We demonstrate the applicability of our methodology through simulations and real data examples. K E Y W O R D Sgraph inference, graph matching, graph mining, seeded graph matching, stochastic block model, vertex nomination Abbreviations: SGM, seeded graph matching; VN, vertex nomination; VOI, vertex of interest.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Graph Matching via Optimal Transport

“…For example, researchers are often concerned with finding a "soft-matching", or a list of potential matches for each vertex of interest. Previous approaches [8,19] to this so-called vertex nomination problem have performed many restarts of the FAQ algorithm with various initial parameters, and then computed the probability that one vertex was matched to another. Since GOAT deals with soft matchings (i.e.…”

Graph matching beyond perfectly-overlapping Erdős–Rényi random graphs

“…In terms of the underlying models, despite the large amount of algorithms proposed over the years, the majority of the efforts are on the Erdős-Rényi random graphs (Erdös and Rényi 1959), which are fundamental but unrealistic. Beyond the Erdős-Rényi random graphs, Patsolic et al (2017) studied the graph matching in a random dot product graph (see e.g. Young and Scheinerman 2007) framework.…”

“…In the sequel, we will refer to these two situations as perfectly-overlapping and partially-overlapping. Work on the latter includes the following: Pedarsani and Grossglauser (2011) studied the privacy of anonyized networks; Kazemi et al (2015) defined a cost function for structural mismatch under a particular alignment and established a threshold for perfect matchability; and Patsolic et al (2017) provided a vector of probabilities of possible matchings.…”

Vertex nomination, consistent estimation, and adversarial modification

“…Given graphs G 1 and G 2 and vertices of interest V * ⊂ V (G 1 ), the aim of the vertex nomination (VN) problem is to rank the vertices of G 2 into a nomination list with the corresponding vertices of interest concentrating at the top of the nomination list. In recent years, a host of VN procedures have been introduced (see, for example, [14,30,26,17,37,48]) that have proven to be effective information retrieval tools in both synthetic and real data applications. Moreover, recent work establishing a fundamental statistical framework for VN has led to a novel understanding of the limitations of VN efficacy in evolving network environments [27].…”

“…Recall that the vertex nomination problem can be stated loosely as follows: given graphs G 1 and G 2 and vertices of interest V * ⊂ V (G 1 ), rank the vertices of G 2 into a nomination list with the corresponding vertices of interest concentrating at the top of the nomination list (see Definition 10 for full detail). While vertex nomination has found applications in a number of different areas, such as social networks in [37] and data associated with human trafficking in [17], there are relatively few results establishing the statistical properties of vertex nomination. In [17], consistency is developed within the stochastic blockmodel random graph framework, where interesting vertices were defined via community membership.…”