Cascade processes in directed complex networks - Vieira, Emanuel Sousa (2018)
In this thesis we study analytically and numerically the bootstrap percolation process in random uncorrelated directed complex networks. We formulate and analyze the bootstrap percolation process on both unweighted and weighted networks and also study a probability based percolation process. The considered percolation process has an associated activation threshold k where a node only gets active if it has at least k active neighboring nodes. We compare our results with analytical and numerical results obtained for undirected complex networks. We also analyze how topological properties of the directed network components, such as the giant strongly connected component and the periphery, influence on the bootstrap percolation process. We apply our theoretical approach for studying the bootstrap percolation on real complex networks. We show that our theoretical approach developed for the case of random uncorrelated directed networks is in a good agreement with numerical simulations of the bootstrap percolation process on real complex networks which actually are correlated and clustered.