Knowing a network by walking on it: emergence of scaling

TL;DR

This paper introduces a network growth model where new nodes attach to existing nodes and explore the network, revealing a phase transition from finite to power-law connectivity distributions, with implications for understanding real networks.

Contribution

The paper presents a novel network growth model with exploration dynamics, deriving its phase diagram and identifying a transition to scale-free structures.

Findings

Identifies a phase transition from finite to power-law degree distributions.

Derives the phase diagram of the proposed network model.

Finds agreement with empirical measurements on real networks.

Abstract

A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two limiting cases and numerical simulations the phase diagram of the model is obtained. In the stationary limit, large network sizes, a phase transition from a network with finite average connectivity to a network with a power law distribution of connectivities, with no finite average, is found. Results are compared with measurements on real networks.