In order to construct the interdependent modular networks, first, two isolated networks labeled A and B was generated and both A and B are small-world modular networks[3, 46], where each modular has the Watts-Strogatz(WS) networks structure[5]. Without loss of generality, the two networks are designed with the same number of nodes NA=NB=N. Then, we coupled the two isolated networks with a certain preferences.
Watts and Strogatz in their seminal paper discovered that many real-world networks are neither random nor regular but somewhere in between, and they proposed a method for constructing such networks, i.e., WS networks[5]. Given that, we created the small-world modular networks model as follows. First, M isolated modules, each with the WS structure, are constructed, In order to generate such networks, we used the random rewiring algorithm proposed by Watts–Strogatz[5], Considering a ring graph with n nodes each connected to its m-nearest neighbours by undirected links. The total number of the links are Q=2mn. The rewiring algorithm includes Q steps, and at each step i, link i are chosen and rewired to a node randomly chosen over the graph with the intra-modular rewiring probability P, provided that multi-link and self-loops are prohibited. The probability P is the intra-modular rewiring probability in this modular network. …show more content…
Namely, the selected intra-modular links are broken and a connection is generated between a randomly chosen
Watts and Strogatz in their seminal paper discovered that many real-world networks are neither random nor regular but somewhere in between, and they proposed a method for constructing such networks, i.e., WS networks[5]. Given that, we created the small-world modular networks model as follows. First, M isolated modules, each with the WS structure, are constructed, In order to generate such networks, we used the random rewiring algorithm proposed by Watts–Strogatz[5], Considering a ring graph with n nodes each connected to its m-nearest neighbours by undirected links. The total number of the links are Q=2mn. The rewiring algorithm includes Q steps, and at each step i, link i are chosen and rewired to a node randomly chosen over the graph with the intra-modular rewiring probability P, provided that multi-link and self-loops are prohibited. The probability P is the intra-modular rewiring probability in this modular network. …show more content…
Namely, the selected intra-modular links are broken and a connection is generated between a randomly chosen