Collections of networks are at the core of modern society, spanning technological, biological and social systems. Over the past decade a "science of networks" has been emerging which blends ideas from statistical physics, applied math, computer science and social sciences. This new science has provided insights into the structure and function of many diverse types of systems, such as protein-interactions in a cell, collaboration networks of scientists, and the World Wide Web. Here we will provide an brief overview of the field, highlighting in particular how mathematical models of random graphs allow us to understand aspects of these real-world systems. The focus is on predicting phase transitions on networks, when a small change in an environmental variable radically alters the structure of a network. Likewise, another important challenge is that distinct networks interact, such as the Internet and the electric power grid. Each network on its own is, in part, a complex system shaped by the collective action of individual agents and interactions between networks can lead to unanticipated consequences, such as cascading failures and novel phase transitions. Also highlighted in this talk will be how random graphs can be use to model the consequences of interdependence between distinct networked systems.
(Recorded on 5 November 2014)
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