Shortest path discovery of complex networks

TL;DR

This paper provides an analytical framework for understanding shortest-path sampling in complex networks, revealing how sampled network properties differ from traditional models and offering formulas for edge discovery probabilities.

Contribution

It introduces new analytic formulas for edge discovery in sampled networks and shows how sampled degree distributions resemble networks with randomly removed edges.

Findings

Number of discovered edges scales slower than mean field predictions.

Sampled degree distributions are similar to networks with random edge removal.

Provides formulas for edge discovery probability in evolving and static networks.

Abstract

In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network model. We also show that the number of discovered edges in a finite network scales much slower than predicted by earlier mean field models. Finally, we calculate the degree distribution of sampled networks, and we demonstrate that they are analogous to a destructed network obtained by randomly removing edges from the original network.