  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.
