Non Parametric Statistics of Dynamic Networks with distinguishable nodes

TL;DR

This paper develops nonparametric statistical methods for analyzing sequences of dynamic networks with labeled nodes, introducing concepts like network depth, and applying techniques such as testing, classification, and principal component analysis.

Contribution

It introduces novel nonparametric tools for dynamic network analysis, including notions of network center and depth, with applications to classification and principal component analysis.

Findings

Development of network depth and center concepts

Statistical techniques for testing and classification of network sequences

Application to real data demonstrating method effectiveness

Abstract

The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks sequences with a fixed number of labeled nodes and study some statistical problems in a nonparametric framework. We introduce natural notions of center and a depth function for networks that evolve in time. We develop several statistical techniques including testing, supervised and unsupervised classification, and some notions of principal component sets in the space of networks. Some examples and asymptotic results are given, as well as two real data examples.