A series of real networks invariants

TL;DR

This paper introduces a series of new Laplacian-based invariants for real networks, which follow exponential or power-law distributions, distinguishing them from artificial networks.

Contribution

It generalizes existing invariants by proposing a series of Laplacian-based centralities with characteristic distribution patterns for real networks.

Findings

Laplacian-based invariants follow exponential distributions in real networks.

For j=0, the invariants follow a power-law distribution.

Different distributions are observed for artificial networks.

Abstract

In this article we propose a generalization of two known invariants of real networks: degree and ksi-centrality. More precisely, we found a series of centralities based on Laplacian matrix, that have exponential distributions (power-law for the case $j = 0$) for real networks and different distributions for artificial ones.