A new kind of node centrality in directed weighted networks based on the demands of network clients

To reveal the correlation between the demands of network clients and the safety and robustness of real-world networks, we propose client demand centrality (CDC) in order to quantify the contributions of nodes in the transportation processes in directed weighted networks. CDC is defined by incorporating not only the topology and dynamics of the network but also the demands of network clients. The centrality measures node potential to ensure acceptable and successful transportation for clients and does quite well in distinguishing the roles of different nodes in the network. Simulation results show that node CDC has Gaussian distributions in directed networks with different link weight distributions, and the expected value of the Gaussian distribution increases from negative to positive with a decrease of the client demand. In particular, for directed scale-free networks with the scale-free link weight distribution, the network CDC is only correlated with the degree structure of the network when the client demand is large.