Extended h-Index Parameterized Data Structures for Computing Dynamic Subgraph Statistics

TL;DR

This paper introduces parameterized data structures based on the h-index to efficiently maintain subgraph frequencies in dynamic graphs, extending previous work to directed and larger subgraphs, with applications in bioinformatics and social networks.

Contribution

It extends existing data structures for subgraph counting to directed graphs and larger subgraphs, achieving efficient update times based on the h-index.

Findings

Directed 3-vertex subgraph counts maintained in O(h) amortized time.

Undirected 4-vertex subgraph counts maintained in O(h^2) amortized time.

Enables new applications in bioinformatics and social network analysis.

Abstract

We present techniques for maintaining subgraph frequencies in a dynamic graph, using data structures that are parameterized in terms of h, the h-index of the graph. Our methods extend previous results of Eppstein and Spiro for maintaining statistics for undirected subgraphs of size three to directed subgraphs and to subgraphs of size four. For the directed case, we provide a data structure to maintain counts for all 3-vertex induced subgraphs in O(h) amortized time per update. For the undirected case, we maintain the counts of size-four subgraphs in O(h^2) amortized time per update. These extensions enable a number of new applications in Bioinformatics and Social Networking research.