Small Worlds: The Dynamics of Networks between Order and Randomness
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Cites background from "Small Worlds: The Dynamics of Netwo..."
...A measure of the typical separation between two nodes in the graph is given by the average shortest path length, also known as characteristic path length, defined as the mean of geodesic lengths over all couples of nodes [5,28]:...
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...The first works on conditions and effects of synchronization in complex networks were reported by Watts [5] and Barahona and Pecora [433]....
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...Watts’ pioneering book on the subject deals with the structure and the dynamics of small-world networks [5], while Strogatz’ review article in the Nature’s special issue on complex systems contains a discussion on networks of dynamical units [1]....
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...The small-world property has been observed in a variety of other real networks, including biological and technological ones [5,28,40,52], and is an obvious mathematical property in some network models, as for instance in random graphs....
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...[5] Watts has considered graphs in which the nodes can connect with either a uniform or a Gaussian probability distribution to other nodes within a finite spatial distance /....
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Cites methods from "Small Worlds: The Dynamics of Netwo..."
...Studies on synchronization in complex topologies where each node is considered to be a Kuramoto oscillator, were first reported for WS networks (Hong et al., 2002; Watts, 1999) and BA graphs (Moreno and Pacheco, 2004; Moreno et al....
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2,669 citations