Data mining when each data point is a network

TL;DR

This paper explores methods for applying data mining to graph-structured data by defining similarity metrics based on subgraph densities and spectral information, enabling analysis of graph ensembles and dynamic networks.

Contribution

It introduces practical solutions for measuring graph similarity and demonstrates their application in analyzing graph ensembles and network evolution.

Findings

Effective graph similarity metrics based on subgraph densities and spectral info

Application to diverse graph datasets including evolving networks

Enhanced scientific computation of network dynamics

Abstract

We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of modeling contexts, especially when coarse-graining the detailed graph information is of interest. One of the main challenges in mining graph data is the definition of a suitable pairwise similarity metric in the space of graphs. We explore two practical solutions to solving this problem: one based on finding subgraph densities, and one using spectral information. The approach is illustrated on three test data sets (ensembles of graphs); two of these are obtained from standard graph generating algorithms, while the graphs in the third example are sampled as dynamic snapshots from an evolving network simulation. We further incorporate these approaches with equation free techniques, demonstrating how such data mining approaches can enhance scientific computation of network evolution dynamics.