Connectivity of growing random networks.

By P. L. Krapivsky, Sidney Redner, F. Leyvraz. Physical Review Letters, 2000

1,062 citations recorded by the source corpus.

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately k(gamma), different behaviors arise for gamma<1, gamma>1, and gamma = 1. For gamma<1, the number of sites with k links, N(k), varies as a stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A(k) approximately k, the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d50a4c23e4ab0d3cf81d1f849d97bf17bb3d29e8

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Citations in the corpus

Accessibility of Cities in the Digital Economy (2004, background): “s the fact that species (and genera) become extinct. However, it has been adapted and generalized by others to explain power laws in many other systems, most famously city sizes [36], paper citations [51, 52], and links to pages on the world wide web [53, 54]. The most general form of the Yule proce”
Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network (2013, background): “Here, we investigate the nonlinear preferential attachment model [31], where the probability that a new link connects to node v is where k v is the indegree of node v , and α > 0.”
Modeling the Internet's large-scale topology (2001, background): “For example, several studies have established that the value of the degree exponent g can be tuned by changing the model parameters 14,21,22,23 , as the relative frequency of node and link addition and removal jointly determine g .”
Power laws, Pareto distributions and Zipf's law (2005, background): “However, it has been adapted and generalized by others to explain power laws in many other systems, most famously city sizes [35], paper citations [50, 51 ], and links to pages on the world wide web [52, 53].”
Statistical mechanics of complex networks (2001, methodology): “(126) corresponds to an asymptotically linear preferential attachment, a correspondence can be made with the model of Krapivsky, Redner, and Leyvraz (2000) as well.”
The Matthew effect in empirical data (2014, background): “Although this setup is rather frail as any nonlinearity in the attachment rate may either eliminate the hubs or generate super-hubs [33, 34], the concept of preferential attachment, along with the “small-world” model by Watts and Strogatz [35], undoubtedly helped usher in the era of network science ”
Showing your ID: intrinsic disorder as an ID for recognition, regulation and cell signaling (2005, background): “This observation suggests a molecular basis for the ‘rich-get-richer’ accretion scenario proposed by Krapivsky et al. (2000) and Barabasi and Oltvai (2004).”
The science of science: from the perspective of complex systems (2017, background): “(3) can be modified to become a directed case when it is written as follows: P(j ! i) = (kin i + 1)/( P lk in l + 1) where kin i denotes the in-degree of node i [107].”