Weighted scale-free network in financial correlations

While many scale-free (SF) networks have been introduced recently for complex systems, most of them are binary random graphs. Here we introduce a weighted SF network in associated with the cross-correlations in stock price changes among the S&P 500 companies, where all vertices (companies) are fully connected and each edge has nonuniform weight given by the covariance between the-two returns connected, normalized by their volatilities. Influence-strength (IS) is defined as the sum of the weights on the edges incident upon a given vertex. Then the IS distribution in its absolute magnitude \q\ exhibits a SF behavior, P-I(\q\) similar to \q\(-eta) with the exponent eta approximate to 1.8(1).