Title:

On the sizes of connected components in a random coloured graph

Abstract:

The random graph model in which the degree of a node is given by a known random variable is called the configuration model. Since one is free to chose how the node degrees are distributed, the configuration model provides a flexible means of mathematical modelling. In this talk, I will further widen this freedom by considering a generalisation of the configuration model in which edges are coloured with N colours, and therefore, node degrees are distributed according to an N-variate random variable. I will then establish the connection between this random variable and the distribution of the sizes of connected components, and demonstrate these results on appealing examples.

More information in:

I.Kryven, Nature Communications 10, 404 (2019).https://doi.org/10.1038/s41467-018-08009-9