Distance Preserving Graph Simplification

TL;DR

This paper introduces the gate graph, a novel graph simplification method that preserves non-local shortest-path distances through local walks, enabling easier visualization and understanding of large graphs.

Contribution

It presents a new gate graph approach, characterizes the gate-vertex set discovery problem, and offers an efficient algorithm with proven bounds for graph simplification.

Findings

Effective preservation of non-local distances in simplified graphs

Efficient algorithm with logarithmic bound for gate-vertex set discovery

Demonstrated effectiveness on real and synthetic graphs

Abstract

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph. Specifically, we construct a gate graph from a large graph so that for any "non-local" vertex pair (distance higher than some threshold) in the original graph, their shortest-path distance can be recovered by consecutive "local" walks through the gate vertices in the gate graph. We perform a theoretical investigation on the gate-vertex set discovery problem. We characterize its computational complexity and reveal the upper bound of minimum gate-vertex set using VC-dimension theory. We propose an efficient mining algorithm to discover a gate-vertex set with guaranteed logarithmic bound. We further present a fast technique for pruning redundant edges in a gate graph. The detailed experimental results using both real and synthetic graphs demonstrate the effectiveness and efficiency of our approach.