Physics (Internal)

Generalized Percolation on Random Graphs

This event is part of the Preliminary Oral Exam.

Examining Committee: H.E. Stanley, Shlomo Havlin, Shyam Erramilli, Kevin Black

Abstract:

Percolation model has been studied extensively for its simplicity and its rich phase transition behaviors. Percolation model on random graphs is a good representation of the attacking process on complex networks and thus provides insight into the study of the robustness of complex systems. Most previous studies have been focusing on random attack, where each node in the graph exists independently with the same probability. We propose a generalized percolation model on random graphs which describes the non-independent local attacking process. We show the theoretical framework and data from simulations agree well with each other. We compare order parameter and percolation threshold with the random attack model. We also show the critical exponents near phase transition and their deviation from the mean-field theory due to the heterogeneity of the random graphs.