Robustness and Vulnerability of Scale-Free Random Graphs

By Béla Bollobás, Oliver Riordan. Internet Mathematics, 2004

319 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e6cacc7a3f82c9f18c1d30c4893c74a8171bf6e8

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Citations in the corpus

A proof of a conjecture of Buck, Chan, and Robbins on the expected value of the minimum assignment (2005, background): “A somewhat similar, although less surprising, phenomenon was studied in [ 6 ], where for a dierent model it was shown that for every positive value of the appropriate parameter c there is a giant component, but its normalized size has all derivatives zero at c = 0. Nevertheless, a gentle increase at”
Graph theory and networks in Biology. (2006, unknown): “In this subsection, we shall discuss four classical concepts of centrality which have recently been applied to biological interaction networks: (i) Degree centrality; (ii) Closeness centrality; (iii) Betweenness centrality; (iv) Eigenvector centrality.”
Why rumors spread so quickly in social networks (2012, background): “Famous structural results prove a small diameter of such graphs [10], determine their degree distribution [11], show high expansion properties [24], and a high robustness against random damage, but a vulnerability against malicious attacks [8, 9, 15, 18].”
Information diffusion through blogspace (2004, background): “This question has been considered from the perspective of rror toleranceof networks like the Internet: what happens to the network if a random (1− ε)-fraction of the links in the Internet fail? Many researchers have observed that power-law networks exhibit extremely high error tolerance [2; 7].”
The phase transition in inhomogeneous random graphs (2005, background): “Other branching processes, and other functional equations, appear when studying random graphs with dependencies between edges, as in [22, 25, 84], but will not be considered here.”
Network resilience (2020, background): “Single real networks, like Internet, are vulnerable to targteted attacks [607, 833].”
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (2005, methodology): “22] that are claimed to form “the basis of network science,” and include (1) classical random graphs due to Erdös and Renyı́ [39]; (2) equilibrium random graphs with a given degree distribution such as the Generalized Random Graph (GRG) method [31]; (3) “small-world networks” due to Watts and Stroga”