SimRank Computation on Uncertain Graphs

TL;DR

This paper extends SimRank similarity computation to uncertain graphs using a novel random walk model, proposing three algorithms that balance accuracy and efficiency, validated through extensive experiments.

Contribution

It introduces a new random walk formulation for SimRank on uncertain graphs and develops three algorithms to compute similarities efficiently.

Findings

The new random walk model satisfies Markov property on uncertain graphs.

Existing algorithms for deterministic graphs are inapplicable to uncertain graphs.

The proposed algorithms achieve high accuracy and efficiency, validated by experiments.

Abstract

SimRank is a similarity measure between vertices in a graph, which has become a fundamental technique in graph analytics. Recently, many algorithms have been proposed for efficient evaluation of SimRank similarities. However, the existing SimRank computation algorithms either overlook uncertainty in graph structures or is based on an unreasonable assumption (Du et al). In this paper, we study SimRank similarities on uncertain graphs based on the possible world model of uncertain graphs. Following the random-walk-based formulation of SimRank on deterministic graphs and the possible worlds model of uncertain graphs, we define random walks on uncertain graphs for the first time and show that our definition of random walks satisfies Markov's property. We formulate the SimRank measure based on random walks on uncertain graphs. We discover a critical difference between random walks on uncertain graphs and random walks on deterministic graphs, which makes all existing SimRank computation algorithms on deterministic graphs inapplicable to uncertain graphs. To efficiently compute SimRank similarities, we propose three algorithms, namely the baseline algorithm with high accuracy, the sampling algorithm with high efficiency, and the two-phase algorithm with comparable efficiency as the sampling algorithm and about an order of magnitude smaller relative error than the sampling algorithm. The extensive experiments and case studies verify the effectiveness of our SimRank measure and the efficiency of our SimRank computation algorithms.