Triadic First-Order Logic Queries in Temporal Networks

2025-07-23

AI Summary

This work addresses the limited expressiveness of conventional temporal triplet queries in temporal networks by proposing a first-order logic (FOL)-based triplet query framework supporting thresholded quantification. The framework uniquely unifies existential and thresholded universal quantifiers within temporal graph querying, significantly enhancing the semantic expressiveness of motif discovery. To realize this, the authors introduce FOLTY—a novel, efficient algorithm that integrates temporal-aware indexing, sparse-graph-optimal traversal strategies, and quantified condition verification mechanisms, achieving theoretically optimal time complexity. Experimental evaluation demonstrates that FOLTY processes temporal graphs with up to 70 million edges within one hour on commodity hardware, exhibiting superior performance and strong scalability.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Temporal Planning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Topic discovery and tracking

Abstract

Motif counting is a fundamental problem in network analysis, and there is a rich literature of theoretical and applied algorithms for this problem. Given a large input network $G$, a motif $H$ is a small "pattern" graph indicative of special local structure. Motif/pattern mining involves finding all matches of this pattern in the input $G$. The simplest, yet challenging, case of motif counting is when $H$ has three vertices, often called a "triadic" query. Recent work has focused on "temporal graph mining", where the network $G$ has edges with timestamps (and directions) and $H$ has time constraints. Inspired by concepts in logic and database theory, we introduce the study of "thresholded First Order Logic (FOL) Motif Analysis" for massive temporal networks. A typical triadic motif query asks for the existence of three vertices that form a desired temporal pattern. An "FOL" motif query is obtained by having both existential and thresholded universal quantifiers. This allows for query semantics that can mine richer information from networks. A typical triadic query would be "find all triples of vertices $u,v,w$ such that they form a triangle within one hour". A thresholded FOL query can express "find all pairs $u,v$ such that for half of $w$ where $(u,w)$ formed an edge, $(v,w)$ also formed an edge within an hour". We design the first algorithm, FOLTY, for mining thresholded FOL triadic queries. The theoretical running time of FOLTY matches the best known running time for temporal triangle counting in sparse graphs. We give an efficient implementation of FOLTY using specialized temporal data structures. FOLTY has excellent empirical behavior, and can answer triadic FOL queries on graphs with nearly 70M edges is less than hour on commodity hardware. Our work has the potential to start a new research direction in the classic well-studied problem of motif analysis.

Problem

• Counting triadic motifs in temporal networks
• Introducing thresholded FOL for richer network queries
• Designing efficient algorithm for FOL triadic queries

Innovation

• Thresholded FOL for temporal motif analysis
• FOLTY algorithm for efficient query processing
• Specialized temporal data structures implementation