确定一类无标度模块网络平均距离的另一种方法
An alternative approach to determining average distance in a class of scale-free modular networks
摘要：
当前感兴趣的各种现实生活中的网络同时是无标度和模块化的。在这里，我们分析研究了一类确定性增长的无标度模块网络的平均距离。凭借的递归关系来自网络的自相似结构，我们严格计算这个重要的量，获得一个明确的封闭形式的解决方案，恢复以前的结果，并证实了广泛的数值计算。得到的精确表达式表明，平均距离尺度与网络中的节点数，表明存在小世界行为。我们认为，这种小世界现象来自于网络家庭的特殊结构。
英文摘要：
Various real-life networks of current interest are simultaneously scale-free and modular. Here we study analytically the average distance in a class of deterministically growing scale-free modular networks. By virtue of the recursive relations derived from the self-similar structure of the networks, we compute rigorously this important quantity, obtaining an explicit closed-form solution, which recovers the previous result and is corroborated by extensive numerical calculations. The obtained exact expression shows that the average distance scales logarithmically with the number of nodes in the networks, indicating an existence of small-world behavior. We present that this small-world phenomenon comes from the peculiar architecture of the network family.
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