Robustness of the in-degree exponent for the World-Wide Web

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We consider a stochastic model for directed scale-free networks following power laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with a growth rate p. At each time step, (i) each newly introduced vertex is connected to a constant number of already existing vertices with the probability linearly proportional to in-degree distribution of a selected vertex, and (ii) each existing vertex updates its outgoing edges through a stochastic multiplicative process with mean growth rate of outgoing edges g and its variance sigma(2). Using both analytic treatment and numerical simulations, we show that while the out-degree exponent gamma(out) depends on the parameters, the in-degree exponent gamma(in) has two distinct values, gamma(in)=2 for p>g and 1 for p<g, independent of different parameters values. The latter case has logarithmic correction to the power law. Since the vertex growth rate p is larger than the degree growth rate g for the World-Wide Web (WWW) nowadays, the in-degree exponent appears robust as gamma(in)=2 for the WWW.
Publisher
AMER PHYSICAL SOC
Issue Date
2002-10
Language
English
Article Type
Article
Keywords

DEGREE DISTRIBUTIONS; EVOLVING NETWORKS; INTERNET TOPOLOGY; DYNAMICS; GRAPHS

Citation

PHYSICAL REVIEW E, v.66, no.4

ISSN
1539-3755
URI
http://hdl.handle.net/10203/83957
Appears in Collection
PH-Journal Papers(저널논문)
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