Efficient Historical Butterfly Counting in Large Temporal Bipartite Networks via Graph Structure-aware Index

TL;DR

This paper introduces a novel graph structure-aware indexing method for efficient historical butterfly counting in large temporal bipartite networks, significantly improving speed and memory efficiency over existing algorithms.

Contribution

The paper proposes two new indices and a combined indexing approach tailored for temporal bipartite graphs, enabling fast butterfly counting with reduced memory usage, especially effective on power-law graphs.

Findings

Outperforms existing methods by up to five orders of magnitude in speed.

Reduces memory footprint while maintaining high query performance.

Theoretically advantageous for power-law bipartite graphs.

Abstract

Bipartite graphs are ubiquitous in many domains, e.g., e-commerce platforms, social networks, and academia, by modeling interactions between distinct entity sets. Within these graphs, the butterfly motif, a complete 2*2 biclique, represents the simplest yet significant subgraph structure, crucial for analyzing complex network patterns. Counting the butterflies offers significant benefits across various applications, including community analysis and recommender systems. Additionally, the temporal dimension of bipartite graphs, where edges activate within specific time frames, introduces the concept of historical butterfly counting, i.e., counting butterflies within a given time interval. This temporal analysis sheds light on the dynamics and evolution of network interactions, offering new insights into their mechanisms. Despite its importance, no existing algorithm can efficiently solve the historical butterfly counting task. To address this, we design two novel indices whose memory footprints are dependent on #butterflies and #wedges, respectively. Combining these indices, we propose a graph structure-aware indexing approach that significantly reduces memory usage while preserving exceptional query speed. We theoretically prove that our approach is particularly advantageous on power-law graphs, a common characteristic of real-world bipartite graphs, by surpassing traditional complexity barriers for general graphs. Extensive experiments reveal that our query algorithms outperform existing methods by up to five magnitudes, effectively balancing speed with manageable memory requirements.