Space Time Dependent Phenomena in Networks

Complex web like structures or networks describe a wide variety of systems ranging from the Internet to the world wide web (WWW), and from social bondings to gene transcriptions. It has been found that these networks that are apparently so diverse in nature, actually possess some important common features like small world property, scale free nature etc. In this book, we have considered growing networks, where the attachment probability of a new node joining the network depends on the degree of the existing nodes along with the "age" and/or "distance" between nodes. Both numerically simulated aging networks as well as real world networks have been considered. In case of aging networks, we have considered a model which is parametrically defined and obtained a rich phase diagram in the parameter space. We have also successfully modelled the citation network, the collaboration network and the earthquake network in which the aging factor is present and from these models several features of the real networks could be reproduced. Finally we have studied how a static phase transition effects the dynamical phenomena of searching or navigation on a network following different strategies.