Fast Graphlet Transform of Sparse Graphs

TL;DR

This paper presents a fast, efficient method for exact graphlet transform in large sparse graphs, enhancing network analysis capabilities with low memory use and high computational speed.

Contribution

The paper introduces a novel fast algorithm for exact graphlet transform in large sparse graphs, addressing computational complexity and enabling advanced network analysis.

Findings

Achieved high computational efficiency in graphlet transform

Reduced memory consumption compared to previous methods

Facilitated high-performance implementation and application

Abstract

We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at multiple granularity levels for classifying vertices on the same graph/network as well as for making differentiation or connection across different networks. Network/graph analysis using graphlets has growing applications. We recognize the universality and increased encoding capacity in using multiple graphlets, we address the arising computational complexity issues, and we present a fast method for exact graphlet transform. The fast graphlet transform establishes a few remarkable records at once in high computational efficiency, low memory consumption, and ready translation to high-performance program and implementation. It is intended to enable and advance network/graph analysis with graphlets, and to introduce the relatively new analysis apparatus to graph theory, high-performance graph computation, and broader applications.