Complex systems are omnipresent in nature and society. Food webs, social networks, power grids, transportation systems, the Internet: all represent networks of entities that can be connected in a variety of ways. Sometimes these networks are disturbed: entities or connections between them are lost and the network’s functioning is affected. Which are the factors that determine how likely this is, and how serious the consequences? Can we use this knowledge to predict and prevent failures?
To answer these questions, scientists often make theoretical representations of these complex systems. One way of doing this is by modelling 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,” says PhD researcher Almerima Jamakovic. “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. Real-life networks are much more complex. Computer and communication networks, for instance, comprise physical as well as logical connections, which are closely interrelated.
Jamakovic and her colleagues aim to identify the underlying characteristics that determine the structure and functioning of such networks. “We collect data from many different kinds of systems,” she explains. “We represent them as networks and make quantitative calculations of their characteristics. Then we try to find commonalities. Which are the parameters that make these networks complex?” Very simple examples of such parameters include the average distance between two random nodes (how many steps are needed to connect them) and the average number of connections that each node has.
Jamakovic: “This provides us with insights into what it is that makes a network robust. Removing one node or one connection may have far greater consequences than removing another node or connection. If we understand why this is, we can put a finger on robustness. Hopefully these analyses will help in the future design of networks.”