Index-adaptive Triangle-Based Graph Local Clustering

Motif-based graph local clustering (MGLC) algorithms are gen-erally designed with the two-phase framework, which gets the motif weight for each edge beforehand and then conducts the local clustering algorithm on the weighted graph to output the result. Despite correctness, this frame-work brings limitations on both practical and theoretical aspects and is less applicable in real interactive situations. This research develops a purely local and index-adaptive method, Index-adaptive Triangle-based Graph Local Clustering (TGLC+), to solve the MGLC problem w.r.t. triangle. TGLC+ combines the approximated Monte-Carlo method Triangle-based Random Walk (TRW) and deterministic Brute-Force method Triangle-based Forward Push (TFP) adaptively to estimate the Personalized PageRank (PPR) vector without calculating the exact triangle-weighted transition probability and then outputs the clustering result by conducting the standard sweep procedure. This paper presents the efficiency of TGLC+ through theoretical analysis and demonstrates its effectiveness through extensive experiments. To our knowl-edge, TGLC+ is the first to solve the MGLC problem without computing the motif weight beforehand, thus achieving better efficiency with comparable effectiveness. TGLC+ is suitable for large-scale and interactive graph analysis tasks, including visualization, system optimization, and decision-making.