Heterogeneous network with distance dependent connectivity |
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Authors: | M Medo J Smrek |
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Institution: | (1) Department of Mathematics, Physics and Informatics, Mlynská dolina, 842 48 Bratislava, Slovak Republic;(2) Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland |
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Abstract: | We investigate a network model based on an infinite regular
square lattice embedded in the Euclidean plane where the node
connection probability is given by the geometrical distance of
nodes. We show that the degree distribution in the basic model
is sharply peaked around its mean value. Since the model was
originally developed to mimic the social network of
acquaintances, to broaden the degree distribution we propose
its generalization. We show that when heterogeneity is
introduced to the model, it is possible to obtain fat tails of
the degree distribution. Meanwhile, the small-world phenomenon
present in the basic model is not affected. To support our
claims, both analytical and numerical results are obtained. |
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Keywords: | PACS" target="_blank">PACS 64 60 aq Networks 89 75 Hc Networks and genealogical trees 01 75 +m Science and society |
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