dorsal/arxiv
View SchemaTopological fractal networks introduced by mixed degree distribution
| Authors | Liuhua Zou, Wenjiang Pei, Tao Li, Zhenya He, Yiuming Cheung |
|---|---|
| Categories | |
| ArXiv ID | physics/0612056 |
| URL | https://arxiv.org/abs/physics/0612056 |
| DOI | 10.1016/j.physa.2007.02.060 |
Abstract
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors. However, highly clustered scale-free network, with power-law degree distribution, or small-world network models, with exponential degree distribution, are not self-similarity. We investigate networks growth mechanism of the branching-deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors. It yields high clustering and spectrums of degree distribution ranging from algebraic to exponential, average shortest path length ranging from linear to logarithmic. We observe that the present networks fit well with small-world graphs and scale-free networks in both limit cases (exponential and algebraic degree distribution respectively), obviously lacking self-similar property under a length-scale transformation. Interestingly, we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values. The results present a reliable connection among small-world graphs, scale-free networks and topological fractal networks, and promise a natural way to investigate universal origins of collective behaviors.
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"abstract": "Several fundamental properties of real complex networks, such as the\nsmall-world effect, the scale-free degree distribution, and recently discovered\ntopological fractal structure, have presented the possibility of a unique\ngrowth mechanism and allow for uncovering universal origins of collective\nbehaviors. However, highly clustered scale-free network, with power-law degree\ndistribution, or small-world network models, with exponential degree\ndistribution, are not self-similarity. We investigate networks growth mechanism\nof the branching-deactivated geographical attachment preference that learned\nfrom certain empirical evidence of social behaviors. It yields high clustering\nand spectrums of degree distribution ranging from algebraic to exponential,\naverage shortest path length ranging from linear to logarithmic. We observe\nthat the present networks fit well with small-world graphs and scale-free\nnetworks in both limit cases (exponential and algebraic degree distribution\nrespectively), obviously lacking self-similar property under a length-scale\ntransformation. Interestingly, we find perfect topological fractal structure\nemerges by a mixture of both algebraic and exponential degree distributions in\na wide range of parameter values. The results present a reliable connection\namong small-world graphs, scale-free networks and topological fractal networks,\nand promise a natural way to investigate universal origins of collective\nbehaviors.",
"arxiv_id": "physics/0612056",
"authors": [
"Liuhua Zou",
"Wenjiang Pei",
"Tao Li",
"Zhenya He",
"Yiuming Cheung"
],
"categories": [
"physics.data-an",
"physics.soc-ph"
],
"doi": "10.1016/j.physa.2007.02.060",
"title": "Topological fractal networks introduced by mixed degree distribution",
"url": "https://arxiv.org/abs/physics/0612056"
},
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