A consensus based distributed algorithm to compute
the spectral radius of a network is proposed. The spectral radius
of the graph is the largest eigenvalue of the adjacency matrix, and
is a useful characterization of the network graph. Conventionally,
centralized methods are used to compute the spectral radius, which
involves eigenvalue decomposition of the adjacency matrix of the
underlying graph. Our distributed algorithm uses a simple update
rule to reach consensus on the spectral radius, using only local
communications.We consider time-varying graphs to model packet
loss and imperfect transmissions, and provide the convergence
characteristics of our algorithm, for both static and time-varying
graphs. We prove that the convergence error is a function of principal
eigenvector of adjacency matrix of the graph and reduces as
O(1/t), where t is the number of iterations. The algorithm works
for any connected graph structure.