Laurienti Paul J, Joyce Karen E, Telesford Qawi K, Burdette Jonathan H, Hayasaka Satoru
Department of Radiology, Wake Forest University Health Sciences, Winston-Salem, North Carolina, 27157, USA.
Physica A. 2011 Oct 1;390(20):3608-3613. doi: 10.1016/j.physa.2011.05.011.
There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes.
关于复杂网络有大量文献，描述了社会、生物和技术系统中各单元之间的各种关系。这种由相互连接的节点组成的网络通常是自组织的，在没有任何关于拓扑结构的总体设计的情况下自然出现，但却能实现节点之间的高效交互。在这里，我们表明，这种自组织网络中的节点数量和连接密度呈现幂律关系。我们研究了47个源自各种生物、社会和技术领域的自组织网络的规模和连接密度，发现规模-密度关系遵循跨越6个数量级的分形关系。这一发现表明，无论规模大小，遵循分形缩放的自组织网络中存在一个最优连接密度。
