Random Graphs and Complex Networks

By Remco van der Hofstad. Cambridge Series in Statistical and Probabilistic Mathematics, 2016

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The Brownian limit of separable permutations (2016, neutral): “[21] R. van der Hofstad (2015).”
A topological insight into restricted Boltzmann machines (2016, background): “More formally, a graph sequence ( G N ) N ≥ 1 has a small-world topology, if there is a constant 0 K ∞ such that lim N →∞ p ( L N ≤ KlogN ) = 1 , where L N is the typical shortest path of G N (van der Hofstad, 2016).”
The science of science: from the perspective of complex systems (2017, background): “Regular lattices and random graphs [5] long served as the most important models of graphs.”
Recent advances in percolation theory and its applications (2015, background): “ and Renyi [152, 153, 154, 155] whose work instigated a great amount of research in the eld [156, 157]. Random graphs have been extensively used as a probabilistic approach to study complex networks [158]. Many real-world complex networks such as the Internet [159], social networks [160], disease mo”