Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations.

By A. Vázquez. Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

593 citations recorded by the source corpus.

The linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a general principle based on local rules. In this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules. It is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks. These conclusions are based on both analytical and numerical results for different local rules, including some models already proposed in the literature.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eba0565e42e231a0e3000cd3ccb305fba5531b8b

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Citations in the corpus

Evolution of social-attribute networks: measurements, modeling, and implications using google+ (2012, methodology): “Our model includes two new components, i.e., attribute-augmented preferential attachment and attribute-augmented triangle-closing , which extend the classical preferential attachment [5, 27] and triangle-closing [29, 43, 53, 2], respectively.”
Popularity versus similarity in growing networks (2011, background): “Another popular mechanism enforcing strong clustering is random walks [12, 68].”
Kronecker Graphs: An Approach to Modeling Networks (2008, result): “And, contrary to other models that match thiscombination of network properties (as for example, (Bu and Towsley, 2002; Klemm and Eguı́luz, 2002; Vázquez, 2003; Leskovec et al., 2005b; Zheleva et al., 2009)), Kronecker graphs also lead totractable analysis and rigorous proofs.”
Bipartite Graphs as Models of Complex Networks (2003, unknown): “More recent models [9, 59, 60, 61, 65, 66, 69] have been introduced.”
The Structure and Function of Complex Networks (2003, background): “For example, a number of authors [30, 102, 198, 217, 220, 242, 397, 398, 411, 412] have studied models of network transitivity that make use of “triadic closure” processes.”
Graph evolution: Densification and shrinking diameters (2006, unknown): “d growing network with redirection model [29], which produces graphs with constant diameter and logarithmically increasing average degree [30]. Similar to our Forest Fire Model is the work of Vazquez [48, 49] where ideas based on random walks and recursive search for generating networks were introdu”
Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network (2013, background): “[30] Vázquez, A.”
The science of science: from the perspective of complex systems (2017, background): “Although it is not explicitly addressed in the growing model with copying [109], various studies have noted that feedforward loops can be significantly increased by using this mechanism [9,112].”
An Overview of Social Networks and Economic Applications (2011, background): “While the Watts and Strogatz (1998) model exhibits high clustering and small average distances, it does not match some other characteristics of observed social networks.”
The Economics of Social Networks (2005, background): “…of how many nodes are met at random compared to how many of their neighbors are met is varied, this process spans between one of completely 53See Vazquez (2003) for a related process which also exhibits clustering, where links are formed by rst entering at a randomly selected node and then…”