Middlemen and Contestation in Directed Networks

TL;DR

This paper introduces the concept of contestability in directed networks to measure and analyze the control and robustness of middlemen, critical nodes that facilitate flows, with applications to empirical social networks.

Contribution

It defines node contestability, establishes its equivalence to middlemen, and develops measures for middleman power and robustness, comparing them with existing centrality metrics.

Findings

Middlemen can be quantitatively identified using contestability measures.

Middleman power correlates with traditional centrality but offers new insights.

Robustness measures indicate how network modifications affect middleman control.

Abstract

This paper studies critical nodes or "middlemen" that intermediate flows in a directed network. The contestability of a node is introduced as a network topological concept of competitiveness meaning that an intermediary's role in the brokering of flows in the network can be substituted by a group of other nodes. We establish the equivalence of uncontested intermediaries and middlemen. The notion of node contestability gives rise to a measure that quantifies the control exercised by a middleman in a network. We present a comparison of this middleman centrality measures with relevant, established network centrality measures. Furthermore, we provide concepts and measures expressing the robustness of a middleman as the number of links or nodes that have to be added to or removed from the network to nullify the middleman's power. We use these concepts to identify and measure middleman power and robustness in two empirical networks: Krackhardt's advice network of managers in a medium sized corporation and the well-known Florentine marriage network as a proxy of power brokerage between houses in Renaissance Florence.