School of Mathematical Sciences Colloquium
Des Higham (University of Strathclyde)
Cities: Networks and Scaling laws
People make cities, and the interactions between people create fascinating structures. The network science view of urban life has proved fruitful in several respects.In this talk I will focus on two issues.
First I will look at the use of centrality measures to identify key players in a network. I will show how new algorithms based on nonbacktraking walks offer concrete advantages. Second I will address the common sighting of scaling laws in empirical studies that report a city attribute, such as energy usage or wealth creation, as a function of population size.
I will show how these observations can be accounted for by very generic network-based rules under mild hypotheses. I will give illustrative examples involving geolocated Twitter interaction data.
References:
Nonbacktracking walk centrality for directed networks, F. Arrigo, P. Grindrod, D. J. Higham and V. Noferini, Journal of Complex Networks, 6, 2018, 54--78.
The deformed graph Laplacian and its applications to network centrality analysis, P. Grindrod, D. J. Higham and V. Noferini, SIAM Journal on Matrix Analysis and Applications, to appear.
High modularity creates scaling laws, P. Grindrod and D. J. Higham, in preparation.
A drinks reception will follow the talk.