Communication in Complex Networks

The investigation of properties of networks has many applications and is receiving considerable attention. One of the properties of interest is the communicability, which measures how easy it is for the nodes of a network to communicate with each other, where communication takes place along the edges of the network. We are interested in how sensitive the global communicability is to local changes in the network. There are several reasons for our interest in the sensitivity. For instance, when the edges of a network represent roads, we may be interested in which road(s) to enlarge or make smaller to increase or decrease, respectively, the traffic flow the most. We also are interested in whether blocking a road, or building a new road, will have a large effect on the communicability in a network. In some applications, we might not know of all the edges of a network, and are interested in how this lack of knowledge may affect our measurement of communicability. Experiments with both synthetic and real networks illustrate the performance of the proposed methods.