Integer Networks

Abstract

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 $L\sim \text{ln}N$ or $L\sim \text{lnln}N$. Further more, the integer networks is high clustered, with clustered coefficient $C\approx 0.34$, and display power-law degree distribution of exponent $\gamma \approx 2.4$.

3 pages, 4 figures

References in corpus (4)

• The structure and function of complex networks
• Maximal planar networks with large clustering coefficient and power-law degree distribution
• Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations
• Families and clustering in a natural numbers network

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