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Random graphs with arbitrary degree distributions and their applications

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Random graph theory predicts properties of networks in diverse applications, revealing insights and discrepancies.

The aim is to explore random graphs with arbitrary degree distributions and their applications in real-world networks.
Developed theory focusing on undirected, directed, and bipartite graphs.
Derived exact expressions for phase transitions and component sizes.
Applied theory to real-world graphs like the World Wide Web and collaboration networks.
Identified phase transition point where a giant component first forms.
Calculated mean component size and average distance between vertices.
Highlighted discrepancies in predictions when comparing theory with real network behaviors.

Newman et al. (2001) studied this question.

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