Modelling financial networks with Kronecker graph

Abstract

In my master thesis I will study a model for network generation based on non-standard operation of matrix multiplication known as Kronecker product. Kronecker product of two graphs is corresponds to a Kronecker product of two adjacency matrices. The model of Kronecker graph, first introduced in [Leskovec et al., 2005] and further studied in [Leskovec et al., 2010] is designed iteratively. As in a classic random graph models, Kronecker graph can be extended to a random version by introducing the probabilities for 0 and 1 in the initiator matrix, the result is a generalization of Erdös-Rényi model. Empirical experiments showed the ability of this model to capture the patterns of real world networks, such as small diameters and heavy-tailed degree distributions. Moreover, Kronecker graph generation allows to model an evolution over time and as there is no fixed correspondence between nodes of the modeled graph with real network’s nodes, the information about real nodes is not revealed.