On Counting Triangles through Edge Sampling in Large Dynamic Graphs

TL;DR

This paper introduces a novel edge sampling framework for dynamic graphs that leverages additional node information to improve triangle counting accuracy and efficiency in evolving networks.

Contribution

It proposes the Edge Sample and Discard (ESD) algorithm, which provides unbiased triangle estimates and adapts to edge updates, outperforming existing methods.

Findings

ESD achieves higher accuracy than state-of-the-art algorithms.

Incorporating neighborhood info improves estimation precision.

Performance varies with graph properties, tested on Barabasi-Albert models.

Abstract

Traditional frameworks for dynamic graphs have relied on processing only the stream of edges added into or deleted from an evolving graph, but not any additional related information such as the degrees or neighbor lists of nodes incident to the edges. In this paper, we propose a new edge sampling framework for big-graph analytics in dynamic graphs which enhances the traditional model by enabling the use of additional related information. To demonstrate the advantages of this framework, we present a new sampling algorithm, called Edge Sample and Discard (ESD). It generates an unbiased estimate of the total number of triangles, which can be continuously updated in response to both edge additions and deletions. We provide a comparative analysis of the performance of ESD against two current state-of-the-art algorithms in terms of accuracy and complexity. The results of the experiments performed on real graphs show that, with the help of the neighborhood information of the sampled edges, the accuracy achieved by our algorithm is substantially better. We also characterize the impact of properties of the graph on the performance of our algorithm by testing on several Barabasi-Albert graphs.