Our society increasingly depends on complex networks such as the Internet, electrical power grids, transportation networks, social networks (friends of friends), ecological networks, etc. Due to their importance to society, complex networks already have received much interest from the research community, ranging from mathematics and computer science to the social and biological sciences. While undoubtedly progress has been made, many crucial aspects of complex networks are not yet sufficiently understood.
Scientists often make theoretical representations of these complex systems. One way of doing this is by modeling their underlying structure – topology – as a network with a collection of nodes and a collection of links that connect pairs of nodes. Imagine for instance a social network, where one person represents a node in the graph. This node is linked to other nodes through the connections that this person has. Each of these nodes is in turn linked to other nodes. This is a relatively simple representation.
We will consider two fundamental properties or a two-fold layering of complex networks: (a) a topology, described as a graph, and (b) a service architecture: the network transports the items for which it is designed, defining the service.
A graph is a set of nodes interconnected by a set of links. The service architecture describes the (time-dependent) function of nodes and links and the protocols/rules that govern interactions and that steer transport of items.
From a topology perspective, the service specifies the links in the graph by link weights (potentially a vector of weights). For instance, an Internet communication link can be characterized by its capacity, delay, distance, loss rate, reliability, etc. Sometimes these networks are disturbed: entities or connections between them are lost and the network’s functioning is affected.
The main goal of this project is to study both graph and link weight structure to design robust networks and to optimize performance.
