MoN18: Eighteenth Mathematics of Networks meeting

Bingsheng Chen (Imperial) Emergence of scaling modular structures through random walks rewiring

It has long been recognised that the development of social networks is controlled by actors playing various different roles. The behaviours of various types of actors in the network will dynamically change the structure of the network, for instance, the scaling behaviour of the community and triadic closure from local motifs.

In this project, we propose a dynamical rewiring model based on the random walks that can reproduce the main statistical characteristics of the real social networks: large clustering coefficients and the emergence of communities. Unlike traditional models with global information like preferential attachment, our model assumes each node will only have local knowledge about their neighbours, which mimic the local researching process in the real world. Our model is able to illustrate that rewiring performed by random walk can break the symmetry and generate the power law like degree distribution. However, community distribution cannot be generated through simple random walk processes. There, we modified the random walk process by adding labels to nodes to count for the heterogeneity of the networks. This process provides us to reproduce the scaling behaviour of communities sizes distribution.

To further support the argument that different types of random walks are necessary while modeling and understanding the networks, measurements of triangle closure are taken. We illustrate a method to detect the mimicking process from triadic closure and explain why two types of random walk mechanisms can better explain the real world data qualitatively compared to a uni-type random walk.

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Contact: Keith Briggs (mailto:keith.briggs_at_bt_dot_com) or Richard G. Clegg (