Extremal Properties of Random Structures

By E. Ben-Naim, Paul L. Krapivsky, Sidney Redner. arXiv.org, 2003

720 citations recorded by the source corpus.

The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety of unusual time dependences and system-size dependences for basic extremal properties are obtained.

Subfields: Geometry and Topology, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ea9ecbb90d04b35675d787be74978f48921b126d

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In Geometry and Topology

In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

Communicability in complex networks. (2007, background): “Their relevance rests on the premise that communication between the nodes takes place through the shortest paths [8-10].”
Measuring the Structure of Road Networks (2007, background): “Entropy has also been widely introduced to measure the heterogeneity of complex networks (Balch, 2000; Ben-Naim et al., 2004).”
Clustering in complex directed networks. (2006, background): “The tendency of a network to form tightly connected neighborhoods (more than in the random uncorrelated case) can be measured by the clustering coefficient (CC), see [11] and [12].”
Power laws, Pareto distributions and Zipf's law (2005, background): “Similar distributions are seen for the number of calls placed by users and also for the numbers of e-mail messages that people send and receive [26, 27].”
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (2005, background): “In addition, it will be useful to understand the way that degree-preserving rewiring causes one to “move” within the space G ( D ) (see for example, [44, 42]).”
JIDT: An Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems (2014, background): “…gained from the application of traditional information-theoretic measures such as entropy and mutual information to study complex systems, for example: proposals of candidate complexity measures [7, 8], characterising order-chaos phase transitions [9–12], and measures of network structure [13, 14].”