  Can one hear the 'sound' of a growing network? We address the problem of
recognizing the topology of evolving biological or social networks. Starting
from percolation theory, we analytically prove a linear inverse relationship
between two simple graph parameters--the logarithm of the average cluster size
and logarithm of the ratio of the edges of the graph to the theoretically
maximum number of edges for that graph--that holds for all growing power law
graphs. The result establishes a novel property of evolving power-law networks
in the asymptotic limit of network size. Numerical simulations as well as
fitting to real-world citation co-authorship networks demonstrate that the
result holds for networks of finite sizes, and provides a convenient measure of
the extent to which an evolving family of networks belongs to the same
power-law class.
