直径约束下的随机网络生长
Random Networks Growing Under a Diameter Constraint
摘要：
我们研究了随机网络的增长的约束下，直径，定义为所有节点之间的平均最短路径长度，保持近似恒定。我们表明，如果图保持其度分布的形式，那么该分布必须近似无标度，指数在2和3之间。直径约束可以被解释为一种环境选择压力，这可能有助于解释图的无标度性质，这些图的数据在其生长的不同时间都是可用的。两个例子包括代表细胞中进化的生物途径和互联网骨干网拓扑结构的图表。我们的假设和解释与这些数据一致。
英文摘要：
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree distribution then that distribution must be approximately scale-free with an exponent between 2 and 3. The diameter constraint can be interpreted as an environmental selection pressure that may help explain the scale-free nature of graphs for which data is available at different times in their growth. Two examples include graphs representing evolved biological pathways in cells and the topology of the Internet backbone. Our assumptions and explanation are found to be consistent with these data.
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