  We study the cross-correlations in stock price changes between the S&P 500
companies by introducing a weighted random graph, where all vertices
(companies) are fully connected, and each edge is weighted. The weight assigned
to each edge is given by the normalized covariance of the two modified returns
connected, so that it is ranged from -1 to 1. Here the modified return means
the deviation of a return from its average over all companies. We define
influence-strength at each vertex as the sum of the weights on the edges
incident upon that vertex. Then we found that the influence-strength
distribution in its absolute magnitude $|s|$ follows a power-law, $P(|s|)\sim
|s|^{-\delta}$, with exponent $\delta \approx 1.8(1)$.
