Emergence of Scaling in Random Networks

By Jannene S. McBride, N. Evans, David D. Lambert, A. Andrew

Subfields: Network Science & Complex Systems

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Citations in the corpus

Neural Execution Engines: Learning to Execute Subroutines (2020, background): “• Barabási–Albert random graphs [2]: A graph of n nodes is grown by attaching new nodes each with m edges that are preferentially attached to existing nodes with high degree.”
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (2005, methodology): “For a number of graph growing models, including the Barab´asi-Albert construction, Aiello et al. show that the evolution process is “scale-free” in the sense of being invariant with respect to time scaling (i.e., the frequency of sampling with respect to the growth rate of the model) and independent”
The application of graph theoretical analysis to complex networks in the brain. (2007, unknown): “A second major discovery was presented in 1999 by Barabási and Albert (Barabasi and Albert, 1999).”
Navigability of interconnected networks under random failures (2013, methodology): “To validate our theoretical predictions, we consider different two-layer multiplex topologies, where each layer can be a Barabási–Albert (BA) network (32), an Erd} os–Rényi (33) or a Watt–Strogatz graph (34).”
Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application (2017, background): “(2) and C(k) deviates from Eqs (6) and (7).”
Revealing strengths and weaknesses of methods for gene network inference (2010, methodology): “We developed unique methodologies to extract lessons from the ensemble of submissions based on the efficacy of the different predictions to learn local connectivity patterns (network motifs (20, 21)), and combinatorial regulation (in-degree distribution (22)).”
Comparison of Characteristics between Region- and Voxel-Based Network Analyses in Resting-State fMRI Data (2009, unknown): “Equally intriguing as small-world networks is a class of complex networks known as scale-free networks (Barabasi and Albert 1999).”
Network ecology: topological constraints on ecosystem dynamics (2004, background): “The recent interest in networks, supported by technics having been intensively developed in th time, gives new keys to better understanding the importance of the network perspective [9,153].”
Growth of preferential attachment random graphs via continuous-time branching processes (2007, background): “We remark this basic model creates a growing “tree” with undirected edges, and includes the “one-edge” case of the original Barabasi-Albert process, made precise in [8], by setting Xi ≡ 1 and β = 0, as well as the “β ≥ 0” scheme considered in [13] and [14], by taking Xi ≡ 1.”