Communities in complex networks

The study of complex networks has attracted the attention of the scientific community for many obvious reasons. A vast number of systems, from the brain to ecosystems, power grid, and the Internet, can be represented as large complex networks, i.e, assemblies of many interacting components with nontrivial topological properties. The link between these components can describe a global behaviour such as the Internet traffic, electricity supply service, market trend, etc. One of the most relevant topological feature of graphs representing these complex systems is community structure which aims to identify the modules and, possibly, their hierarchical organization, by only using the information encoded in the graph topology. Deciphering network community structure is not only important in order to characterize the graph topologically, but gives some information both on the formation of the network and on its functionality.

Networks for Knowledge: Social Media enthuses students of Early Years Education

Networks for Knowledge (n4k Ltd) are a Work Based Learning organisation which specialises in Early Years Education. Training and Development Manager, Elaine Wareing has developed the use of Facebook and Twitter to promote peer learning and interaction beyond the classroom. It also allows trainers to discuss ideas and challengers with a wider group of learners. This has allowed practitioners across a wide geographical area to share their thoughts and ideas together on some of the subjects relating to early years practice.

Forward-looking Pairwise Stability in Networks with Externalities

We consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called a forward-looking network formation scheme if, first, the probability that a link is created is positive if the discounted, expected gains to its two participants are positive, and if, second, the probability that a link is eliminated is positive if the discounted, expected gains to at least one of its two participants are positive. The main result is the existence, for all discount factors and all value functions, of a forward-looking network formation scheme. Furthermore, we can always nd a forward-looking network formation scheme such that (i) the allocation rule is component balanced and (ii) the transition probabilities increase in the di erence in payo s for the corresponding players responsible for the transition. We use this dynamic solution concept to explore the tension between e ciency and stability.