Integer Networks

Details Integer Networks Integer Networks

2004-05-12

arxiv.org/abs/cond-mat/0405258v4

Physica A 367: 613-618 (2006)

Physics

Condensed Matter

Statistical Mechanics

3 pages, 4 figures

Scientific paper

10.1016/j.physa.2005.11.011

Inspired by Pythagoras's belief that numbers are the absolute reality, we obtain some demonstrational results about topological properties of integer networks, in which the vertices represent integers and two vertices are neighbors if and only if there exists a divisibility relation between them. We strictly prove that the diameter of networks has a constant upper bound independent to the network size $N$, which is completely different from the extensively studied real-life networks with their average distance increasing logarithmically to $N$ as $L\sim \texttt{ln}N$ or $L\sim \texttt{lnln}N$. Further more, the integer networks is high clustered, with clustered coefficient $C\approx 0.34$, and display power-law degree distribution of exponent $\gamma\approx 2.4$.

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