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 the N-variate random variable. I will then establish the connection between this random variable and the size distribution of connected components, and discuss the implications of these results to bond pdercolation.

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