A review of "Random graphs and complex networks" by Hofstad

Overview A random graph is a collection of vertices and edges connecting pairs of them at random based on edge probabilities (Newman et al. 2001; Hatano and Mesbahi 2005). The theory of random graphs was introduced by Erdős and Rényi (1960) to give a probabilistic construction of a graph with large girth and large chromatic number after discovering that, in graph theory, probabilistic methods are effective in addressing extremal problems (Bollobás 2001; Frieze and Karoński 2016). The theory of random graphs, thus, lies at the crossroads of probability theory and graph theory (Hatano and Mesbahi 2005). By and large, complex networks have distinctive empirical properties and they grow in an unpredictable manner. From social networks to the World Wide Web to biological networks, challenges are faced in understanding their structure and development. The theory of random graphs is widely used to model and analyze most complex networks for studying their behavior and for capturing the uncertainty and the lack of regularity. Over the past two decades, a volume of random graph models have been developed to capture the behavior of small-world and scale-free complex networks. There are a number of books on the multidisciplinary field of random graphs. Properties of the real-world networks, their models and dynamical processes living on them are partly covered in Janson et al. (2000), Bollobás (2001), Marchette (2004), Durrett (2007), Newman (2010), Frieze and Karoński (2016) and Krivelevich et al. (2016). However, until now, there has been no comprehensive book specifically dealing with random graph models for real-world networks. The book by Remco van der Hofstad fills this gap by studying random graphs as models for complex networks, summarizing the insights Book details Hofstad, R Random Graphs and Complex Networks. vol. 1. New York: Cambridge University Press; 2017. 321 pages; ISBN: 978-1-107-17287-6