Complex network analysis has its origins in the mathematical study of networks, known as graph theory. However, unlike classical graph theory, the analysis primarily deals with real-life networks that are large and complex—neither uniformly random nor ordered, but have a more structured architecture. A network is defined by a collection of nodes (vertices) and links (edges) between pairs of nodes . In Internet, for example, the nodes represent routers and the edges the physical connections between them. In the same way, nodes in large-scale brain networks usually represent brain regions, while links represent anatomical, functional, or effective connections.

Previous research has revealed  that there exist some common structural properties in many real-world networks such as scale-free, small-world and high clustering coefficient. These attributes have important effects on the various types of collective behavior in complex networks such as diffusion and cascading behavior, synchronization, cooperation and network evolution.The interplay between structural properties on the one hand and Collective behavior of interacting agents on networks has attracted a great deal of attention.

DML research laboratory has started research in this area since May 2009. The summary of the domains of activity of this group are:

Network Structure and Models

Finding the statistical properties of network structure and creating models of networks that can help us to understand the meaning of these properties are the one of the major current challenges in complex network research. The main activity of our research in this area is the analysis and characterization of the network’s structure and the development of models aimed at the understanding of the global behavior of these systems.

Information Networks

The complex networks (such as social systems) of interactions among a group of individuals plays a fundamental role in the spread of information and influence. Such effects have been observed in many cases, when an behavior gains sudden widespread popularity. We would like to understand how the structure of the network affects the spread of information, influence and viruses over the network. We monitor the spread of information on the complex networks. We ask what are the typical structural patterns of information propagation? We aim in creating models that help us predict future and identify influential nodes.

Study of Social Networks

In recent years, a considerable amount of research has been done on various topics in online social networks such as Facebook and Flickr. The fast increase in the popularity of these networks has prompted researchers to study how social networks form and evolve over time. This part of our research activity is devoted to investigate the social phenomena on networks. Here we study how the complex structure of social interactions, affects the dynamics of collective behaviour such as the information propagation, the cooperation between selfish individuals, and the emergence of synchronization between interacting agents. Other topics of research concern the study of reselience of network, the detection of community structures, and the efficient search methodes in social networks.

Sampling from Large Networks

Our researches in this area are focused on making inference from partially-observed complex network structures. Most of our current work is about understanding the strengths and limitations of data sampled with link-tracing designs such as snowball sampling, and random walk sampling.

Complex Networks | Digital Media Lab