Structure-dynamics interplay in complex networks

• Lucas Antiqueira
• Bruno Abrahao
• Jonathan Cannon
• Damian Blasi
• Gavin Fay
• Joseph Gran
• Chaitanya Gokhale
• Vanessa Weinberger
• Borys Wrobel

Goal: Analyze and explain correlations between network structure and dynamics.

We have two different trends. The first one has the following features:

• The dynamics is a diffusion process (random walk) occurring on the network.
• The structure is represented by different network models (random, small-world, scale-free).
• Applications? Any network whose dynamical properties are reasonably represented by random walks.
• People interested: Lucas Antiqueira, Damian Blasi (see next paragraph)

Excursus: well, actually what I thought about structure/dynamics was related with linear dynamics near equilibria states of the system. Like I said, any dynamical system that we could imagine behaves, near its equilibrium, like a linear system. The interesting point -I think- is to see how some structural and fixed-in-time properties of the network (from average number of neighbors to mean path length) could change the stability of the fixed point. One real world issue associated with this kind of behavior was formulated in ecology: why do ecosystems hold such a big number of niches when our intuition tell us that more species implies more struggle for resources? There's a lot of bibliography around there, so I' ll suggest to employ the most striking feature of modern societies: division of work. We could use our meeting tomorrow to decide who would read what, so we can then opt between the available strategies...

Second trend:

• The dynamics is related to the network evolution in terms of inclusion of nodes, rewiring of edges, change of nodes/edges properties, etc, etc.
• Motifs play a special role in structural analysis.
• Special attention to food-webs.
• People interested: Jonathan Cannon