Subgraph Search in Large Graphs with Result Diversification

Abstract

The problem of subgraph search in large graphs has wide applications in both nature and social science. The subgraph search results are typically ordered based on graph similarity score. In this paper, we study the problem of ranking the subgraph search results based on diversification. We design two ranking measures based on both similarity and diversity, and formalize the problem as an optimization problem. We give two efficient algorithms, the greedy selection and the swapping selection with provable performance guarantee. We also propose a novel local search heuristic with at least 100 times speedup and a similar solution quality. We demonstrate the efficiency and effectiveness of our approaches via extensive experiments.

Model-Agnostic and Diverse Explanations for Streaming Rumour Graphs

“…• MCS [39]: counts the number of nodes and edges in the maximum common subgraph of two graphs. • Graphsim [38]: extends the MCS measure by incorporating modalities of the data. • Graph edit distance (GED): lifts the idea of the string edit distance to graphs [15].…”

“…As such, our framework defines a retrieval problem, where the relevance of a subgraph s ∈ S, given a subgraph q for which an explanation shall be derived, is derived from the similarity of s and q, denoted by sim(s, q). Various graph similarity measures for inexact graph matching have been proposed in the literature, see [38]. In our framework, the graph similarity measure represents a design choice and the only assumption imposed is that the similarity score is normalized to [0, 1].…”

“…• Graphsim [38]: Graphsim generalizes the concept of a MCS and incorporates data modalities. Based on an isomorphic mapping between nodes of two graphs, the measure compute the Jaccard similarity of their modalities.…”

“…where dist(v, u) = 1 − sim(v, u) is the distance between nodes u and v. We say that a modality a ∈ A is covered by a subgraph s, if there is a node v with the same modality, i.e., φ(v) = a, within distance δ from s, i.e., dist(v, s) ≤ δ, where δ is a distance threshold. By limiting the distance, we ensure that the modality plays a role in information propagation inside the subgraph [38]. Then, we define the influence of this modality as α dist(a,s) , where dist(a, s) is the minimum distance of any node v to s, with φ(v) = a, and α being a decay factor.…”

“…Proofs of the properties of µ C and µ C are omitted due to space constraints. Monotonicity and submodularity of µ then follows from the preservation of these properties by summation [41,38].…”