Funnelling related phase transitions in networks

TL;DR

This paper investigates the funnelling effect in network searches, defining funnelling capacity and identifying phase transitions where the effect appears or disappears based on network parameters.

Contribution

It introduces a formal definition of funnelling capacity and demonstrates the existence of phase transitions in the funnelling effect within networks.

Findings

Funnelling capacity distribution can follow a power law.

A phase transition exists between funnelling and non-funnelling regimes.

Network parameters control the presence of the funnelling effect.

Abstract

Funnelling effect, in the context of searching on networks, precisely indicates that the search takes place through a few specific nodes. We define the funnelling capacity $f$ of a node as the fraction of successful dynamic paths through it with a fixed target. We claim that there is a funnelling effect if the distribution $D(f)$ of the fraction of nodes with funnelling capacity $f$ shows a power law behaviour. We find that a transition from a search with funnelling effect to that without any such effect can exist and is driven by the parameters defining the network.