An alternative approach to determining average distance in a class of scale-free modular networks

作者：Zhang Z*******^*; Lin Yuan

来源：Journal of Statistical Mechanics: Theory and Experiment , 2010, P12017.

DOI：10.1088/1742-5468/2010/12/P12017

• exact results
• random graphs
• networks
• network reconstruction

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 the existence of small-world behavior. We show that this small-world phenomenon comes from the peculiar architecture of the network family.

• 出版日期2010-12
• 单位复旦大学