Classes of small-world networks.

By L. A. Amaral, Antonio Scala, Marc Barthelemy, H. Eugene Stanley. Proceedings of the National Academy of Sciences of the United States of America, 2000

3,090 citations recorded by the source corpus.

We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.

Subfields: Experimental and Cognitive Psychology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/61be22241a09b72c0a1a6d928f2c08aa839ec3f7

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In Statistical and Nonlinear Physics

Citations in the corpus

Evolution of networks (2001, methodology): “In July of 2000, there were about 150 000 routers in the Internet [104].”
Molecular ecological network analyses (2012, background): “Small world network has a small average shortest path (GD) typically as the logarithm of the number of nodes [43].”
Collaboration and Creativity: The Small World Problem1 (2005, neutral): “…interlocks, the Web, power grids, a worm’s brain, the Hollywood actor labor market, commercial airline hubs, and production teams in business firms (Watts 1999; Amaral et al. 2000; Kogut and Walker 2001; Newman 2000, 2001; Davis, Yoo, and Baker 2003; Baum, Shipilov, and Rowley 2003; Burt 2004).”
The spatial structure of networks (2004, background): “Empirical studies of networks, even networks in which geography plays a pivotal role, have, with some exceptions [6, 18, 19, 20], similarly focused almost exclusively on topology [4, 21, 22].”
Clustering and preferential attachment in growing networks. (2001, background): “We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators.”
From Density to Destiny: Using Spatial Dimension of Sales Data for Early Prediction of New Product Success (2004, background): “We have chosen the classic level of 5% as an upper limit, because beyond this level, the social system becomes similar to a random network and less comparable to real-life social systems (Amaral et al. 2000).”
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (2005, background): “Perhaps most importantly, SF graphs are claimed to exhibit a host of startling “emergent” consequences of universal relevance, including intriguing self-similar and fractal properties (see below for details), small-world characteristics [9], and “hub-like” cores.”
The Packet Switching Brain (2011, neutral): “Separate costs may accrue due purely to network connectivity constraints in adding nodes to small-world networks (Amaral, Scala, Barthelemy, & Stanley, 2000 ).”
Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory (2008, neutral): “Commonly for single-scale and broad-scale regime the sharp cutoff functions f(k/kcrit) are exponential or Gaussian (Amaral et al., 2000).”
A Survey of Statistical Network Models (2009, background): “ks. Durrett [91] discusses links between small-world models and stochastic processes. Typical usage of small-world models include empirical analyses involving aggregate summary statistics (see, e.g., [18;231]). There are as yet no formal statistical methods for examining the evolution of small-world”
Models of the Small World (2000, background): “Some other networks, such as the network of movie actors, show similar behavior, but with an exponential cutoff in the power law, while others still, such as true social networks and neural networks, appear to have exponential or Gaussian degree distributions (Amaral et al., 2000).”