Efficient behavior of small-world networks.

By Vito Latora, Massimo Marchiori. Physical Review Letters, 2001

4,792 citations recorded by the source corpus.

We introduce the concept of efficiency of a network as a measure of how efficiently it exchanges information. By using this simple measure, small-world networks are seen as systems that are both globally and locally efficient. This gives a clear physical meaning to the concept of "small world," and also a precise quantitative analysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/f45dce9b51785e2daa9939c1bd00febf1bd787d0

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Citations in the corpus

Characterization of complex networks: A survey of measurements (2005, background): “Latora and Marchiori [67] proposed a closely related measurement that they called global efficiency: E = 1 N(N − 1) ∑”
Human mobility: Models and applications (2017, background): “Apart from this, some of the many aspects studied on intra-urban mobility relate to the typical distance scales of movement [63]; measures of travel duration [340]; effects of population size on the structure and dynamics of mobility [105, 341]; the effect of city topology on the displacements of it”
Dynamic functional reorganization of the motor execution network after stroke. (2010, background): “The Lp of a network is the average minimum number of connections that link any two nodes of the network, which quantifies the ability of parallel information propagation or global efficiency (Latora and Marchiori, 2001) of a network.”
Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory (2009, methodology): “In this way, calculation of L resembles the 'global efficiency' introduced by Latora and Marchiori [44].”
Network Analysis of Intrinsic Functional Brain Connectivity in Alzheimer's Disease (2008, methodology): “Efficiency of a graph (Eglobal-net) [50] is inverse of the harmonic mean of the minimum path length between each pair of nodes, Lij, and was computed as,”
Cognitive Network Neuroscience (2015, background): “A related concept—network efficiency (Latora & Marchiori, 2001, 2003)—is also calculated based on shortest paths through a network, but in this case, a network will have high efficiency if it has a short path length and the network will have low efficiency if it has a long path length.”
Brain graphs: graphical models of the human brain connectome. (2011, background): “In addition to the global efficiency, Latora & Marchiori (2001) also defined the local efficiency of each node, which is similar but not equivalent to its clustering coefficient or fault tolerance (see Figure 3D).”
Modeling the Impact of Lesions in the Human Brain (2009, methodology): “Global efficiency is computed as the average of the inverse distance between all nodes and captures the network’s capacity for communication along short paths [28].”
Cognitive fitness of cost-efficient brain functional networks (2009, methodology): “However, networks derived from brain imaging data are also topologically configured to deliver high global and local efficiency of parallel information transfer (2, 3); this can be equivalently described in terms of short path length and high clustering of brain networks compared with random graphs ”