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Chunk #9 — Materials and methods — Network models

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Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators.
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The network topologies that we consider are Erdös–Rényi random networks, Watts–Strogatz SW networks, Barabási–Albert SF networks, and a super-hub network. A random network is constructed by connecting randomly selected pairs of nodes until the necessary amount of connections (N×k2) are formed (Erdös and Rényi, 1960). A SW network is constructed by rewiring a one-dimensional lattice with a rewiring probability of 0.1 (Watts and Strogatz, 1998). A SF network is constructed as previously reported (Barabási and Albert, 1999), starting with seven fully-coupled nodes as an initial structure (21 connections) and sequentially adding 43 nodes with three connections per node under the preferential attachment rule, i.e., the probability of adding a new connection to an existing node i (1 ≤ i ≤ N′), Π(ki), is given by: Π(ki)=ki/∑j=1N′kj, where N' is the number of existing nodes, and ki the degree of i. A super-hub network comprises three hub nodes that are interconnected and also fully connected to other 47 nodes. Either zero or one connection is assigned between a given pair of nodes, except in the super-hub network, connections between hub nodes