Mathematical Sciences

Dr David B. Penman

Research Interests

A new class of random graphs. Instead of the classical assumption that all edges arise independently of each other, with the same probability, one assumes that each vertex independently receives one of k colours and then the probability that an edge between two vertices arises  depends on the colours of the two vertices. Since the colours of the vertices are assumed hidden, whether or not edges are present are no longer independent of each other: for example, with two equiprobable colours, if edges arise between vertices of the same colour with probability p and between vertices of different colours with probability q, the probability of the triangle 1-2-3-1 arising is  ((p+q)/2)^3+((p-q)/2)^3 rather than ((p+q)/2)^3 as classically. The thrust of the research is to consider the probability of the random graphs in these more general models having various properties, and compare and contrast this with the corresponding probability in that classical model where the overall probability of each edge arising is the same, so that the differences between the two reflect the dependence structure in the new model.

Member of the Computational Combinatorics Group.

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