# MoN17: Seventeenth Mathematics of Networks meeting

## Mixed and time-varying models for evolving complex networks – Naomi Arnold (QMUL)

The last 20 or so years has seen an increase in the prevalence and quality of real network datasets. This is particularly true in the context of communication and online networks, with much progress made in uncovering the Internet’s AS topology, and online social networks often easily crawlable for topological information. We have also seen a wealth of models aimed at capturing the evolution of these network topologies over time, explaining commonly observed structural features, including heavy-tailed degree distributions, small average path lengths and high clustering. Examples of these models include the Barabasi-Albert model and more generalised preferential attachment models.

The majority of models in the literature assume a single model for network growth (e.g. preferential attachment) and one that is unchanging in time. We weaken these assumptions by investigating a modelling framework that allows a weighted combination of multiple models and allows the models to change over time. Firstly, we present a likelihood measure that can serve to quickly find the best weighted model combination for a given network dataset and candidate model components. Using this, we demonstrate in the case of an AS and online social network dataset, that a combination of given modelling elements may provide a better fit than any one alone. Secondly, we present a work in progress extending this framework to address models which may change over time, aimed at detecting and characterising changepoints in a network’s evolution.

Bio: Naomi obtained her Mathematics BA at Murray Edwards College, Cambridge in 2017 and is now a PhD student with the Networks research group at Queen Mary University of London. First captured by networks and complex systems during an undergraduate project on ecosystems with the British Antarctic Survey, her research interests are now in modelling dynamic complex networks. During her first year she has had presentations accepted at the Conference of Complex Systems, the Mediterranean School for Complex Networks and a satellite of the NetSci conference. She also enjoys science outreach, and has given lectures to mathematics undergraduates and high school students on some of the classical, and often surprising results in network study.

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Contact:
Keith Briggs
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or
Richard G. Clegg (richard@richardclegg.org)