Searchability of Networks

Abstract

We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively difficult to search, and thus that the abundance of scale-free networks in nature and society may reflect an attempt to protect local areas in a highly interconnected network from nonrelated communication. In fact, starting from a random node, real-world networks with higher order organization like modular or hierarchical structure are even more difficult to navigate than random scale-free networks. The searchability at the node level opens the possibility for a generalized hierarchy measure that captures both the hierarchy in the usual terms of trees as in military structures, and the intrinsic hierarchical nature of topological hierarchies for scale-free networks as in the Internet.