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| The Structural Properties of Koch Networks Based on Node Labels |
| ZHAI Yinhua,b , WANG Yinhea
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| a. School of Automation, b. School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China |
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Abstract The Koch Fractal Island, which is starting from a regular polygon, is mapped to complex evolving Koch networks. The informative labels are given to nodes, the labels are based on the time and location when nodes are accessing to Koch networks. By the advantages of the informative labels, we get the exact solution of main structural properties of Koch networks, including degree distribution and cumulative degree distribution function, as well as the clustering coefficient, average shortest path length and the correlation function of degree, betweenness centrality and the shortest path routing and length. The results show that, Koch network is a scale-free and small-world network; its clustering coefficient tends to relatively large constant; average shortest path length is proportional to the logarithm of the size of networks; degree correlation function is exponential function relationship with node's degree.
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Received: 15 January 2015
Published: 25 February 2025
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