We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probability proportional to its degree. This process was introduced by Barabási and Albert 3, as a simple model of the growth of real-world graphs such as the world-wide web. Computer experiments presented by Barabási, Albert and Jeong 1,5 and heuristic arguments given by Newman, Strogatz and Watts 23 suggest that after n steps the resulting graph should have diameter approximately log n. We show that while this holds for m=1, for m=2 the diameter is asymptotically log n/log log n.
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Description
Networks with power-law degree distributions have mean geodesic distances that increase no faster than log n/log log n
%0 Journal Article
%1 keyhere
%A Bollobás*, Béla
%A Riordan, Oliver
%D 2004
%J Combinatorica
%K diameter distance geodesic graph mean random
%N 1
%P 5--34
%T The Diameter of a Scale-Free Random Graph
%U http://dx.doi.org/10.1007/s00493-004-0002-2
%V 24
%X We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probability proportional to its degree. This process was introduced by Barabási and Albert 3, as a simple model of the growth of real-world graphs such as the world-wide web. Computer experiments presented by Barabási, Albert and Jeong 1,5 and heuristic arguments given by Newman, Strogatz and Watts 23 suggest that after n steps the resulting graph should have diameter approximately log n. We show that while this holds for m=1, for m=2 the diameter is asymptotically log n/log log n.
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@article{keyhere,
abstract = {We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probability proportional to its degree. This process was introduced by Barabási and Albert [3], as a simple model of the growth of real-world graphs such as the world-wide web. Computer experiments presented by Barabási, Albert and Jeong [1,5] and heuristic arguments given by Newman, Strogatz and Watts [23] suggest that after n steps the resulting graph should have diameter approximately log n. We show that while this holds for m=1, for m=2 the diameter is asymptotically log n/log log n.
ER -},
added-at = {2009-04-06T09:46:06.000+0200},
author = {Bollobás*, Béla and Riordan, Oliver},
biburl = {https://www.bibsonomy.org/bibtex/26a79d370bf4979548ace69b97a61b2d3/folke},
description = {Networks with power-law degree distributions have mean geodesic distances that increase no faster than log n/log log n},
interhash = {16beb80dcc792cb525ee07429731149e},
intrahash = {6a79d370bf4979548ace69b97a61b2d3},
journal = {Combinatorica},
keywords = {diameter distance geodesic graph mean random},
month = {#jan#},
number = 1,
pages = {5--34},
timestamp = {2009-04-06T09:46:06.000+0200},
title = {The Diameter of a Scale-Free Random Graph},
url = {http://dx.doi.org/10.1007/s00493-004-0002-2},
volume = 24,
year = 2004
}