Geometric fractal growth model for scale-free networks
Geometric fractal growth model for scale-free networks
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DOI：
10.1103/physreve.65.056101
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发表时间：
2002-05-01
影响因子：
2.4
通讯作者：
Kahng, B
中科院分区：
文献类型：
--
作者：
Jung, S;Kim, S;Kahng, B
我们引入了一个确定性模型的无标度网络，其度分布遵循幂律与指数伽玛。在每个时间步，每个顶点生成其后代，其数量与该顶点的度成比例，比例常数为m - 1（m >1）。我们考虑两种情况：第一，每个后代只连接到它的父顶点，形成一个树结构。其次，它连接到其父顶点和祖顶点，形成循环结构。我们发现这两个模型在度分布上都表现出幂律行为，其指数为gamma = 1 + ln（2 m- 1）/ln m.因此，通过调整m，可以在范围2 < gamma< 3中调整度指数。我们还解析地求解了树结构的两个顶点之间的平均最短路径距离d，显示了小世界行为，即d类似于ln N/ln（k）over bar，其中N是系统大小，并且（k）over bar是平均度。最后，我们考虑的情况下，后代的数量是相同的所有顶点，并发现度分布表现出指数衰减行为。
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power law with the exponent gamma. At each time step, each vertex generates its offspring, whose number is proportional to the degree of that vertex with proportionality constant m - 1 (m >1). We consider the two cases: First, each offspring is connected to its parent vertex only, forming a tree structure. Second, it is connected to both its parent and grandparent vertices, forming a loop structure. We find that both models exhibit power-law behaviors in their degree distributions with the exponent gamma = 1 + ln(2m- 1)/ln m. Thus, by tuning m, the degree exponent can be adjusted in the range, 2 < gamma< 3. We also solve analytically a mean shortest-path distance d between two vertices for the tree structure, showing the small-world behavior, that is, d similar to ln N/ln (k) over bar, where N is system size, and (k) over bar is the mean degree. Finally, we consider the case that the number of offspring is the same for all vertices, and find that the degree distribution exhibits an exponential-decay behavior.