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

2024-06-01

arXiv.org

AI Summary

Efficiently counting historical butterflies (i.e., 2×2 complete bipartite subgraphs) within arbitrary time windows in temporal bipartite graphs remains a critical bottleneck for analyzing the evolution of dynamic interaction networks. Method: This paper proposes the first real-time historical butterfly counting framework for large-scale temporal bipartite graphs. It introduces two lightweight, butterfly- and wedge-dependent joint indexes, integrating graph-structure-aware indexing, wedge decomposition optimization, time-window pruning, and structure-adaptive index construction—thereby breaking classical complexity lower bounds on power-law-distributed graphs. Contribution/Results: Experiments demonstrate up to 10⁵× speedup in query latency over state-of-the-art methods, significantly reduced memory overhead, and millisecond-scale responses on graphs with up to one billion edges.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Social Networks and Social Media: Social mining and social search on the Web

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.

Problem

• Temporal Bipartite Graphs
• Historical Butterfly Count
• Network Dynamics Analysis

Innovation

• Butterfly Counting
• Memory-efficient Algorithm
• Dynamic Network Analysis