Generating scale free networks in Molecular Biology

Mathematics and Statistics Seminar

Friday November 25 2016

1:30 p.m. - 2:30 p.m.

Physics 103

Generating scale free networks in Molecular Biology

S Konini and EJ Janse van Rensburg*

In this talk a mean field analysis of algorithms used to grow scale free networks is presented. The talk will focus primarily on four widely used algorithms, namely the Barabasi-Albert Algorithm, the Vazquez Algorithm, the Sole Algorithm and the iSite algorithm. With the exception of the Barabasi-Albert Algorithm, these algorithms were introduced to explain or model the evolution of protein-protein interaction networks in Molecular Biology. All four algorithms are based in one way or another on two main elementary moves: growth by random preferential attachment, or by the duplication-divergence of existing nodes. At each time step of the algorithm a new node is created and this causes the growth of the network over time. The implementation of the elementary moves are done to favour an increase in the number of hubs (or nodes of high degree) in the network. Mean field theory for each of the algorithms will be presented, with some numerical result to test the validity of the mean field results. Several variants of the algorithms will also be discussed, generalising the algorithms to wider classes of networks.