Long Range Interactions in Complex Networks

An interaction in a complex network is any kind of information or process that can propagate between network units along network links. Complex networks, which represent the structural skeleton of our societal, technological and infrastructural systems, play a major role in the propagation of processes. It is usually assumed that interactions in networks propagate only from a node to its nearest neighbours. This book is concerned with interactions that can be transmitted from a node to others that are not directly connected to it. We call these interactions long-range interactions (LRI). We focus on the case of infections spreading in networks of social contacts. An infection, in it very broad sense, can be propagated through the network of social contacts among individuals. These contacts include both close contacts and casual encounters among individuals in transport, leisure, shopping. The LRI approach is then implemented in a susceptible-infected-susceptible (SIS) model accounting for the spread of infections in complex networks. A parameter called conductance controls the feasibility of those casual encounters. LRI is also extended to some concepts of complex networks.