Middlemen and Contestation in Directed Networks

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.