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We investigate a factor that can affect the number of links of a specificstock in a network between stocks created by the minimal spanning tree (MST)method, by using individual stock data listed on the S&P500 and KOSPI. Amongthe common factors mentioned in the arbitrage pricing model (APM), widelyacknowledged in the financial field, a representative market index isestablished as a possible factor. We found that the correlation distribution,$\rho_{ij}$, of 400 stocks taken from the S&P500 index shows a very similarwith that of the Korean stock market and those deviate from the correlationdistribution of time series removed a nonlinearity by the surrogate method. Wealso shows that the degree distribution of the MSTs for both stock marketsfollows a power-law distribution with the exponent $\zeta \sim$ 2.1, while thedegree distribution of the time series eliminated a nonlinearity follows anexponential distribution with the exponent, $\delta \sim 0.77$. Furthermore thecorrelation, $\rho_{iM}$, between the degree k of individual stock, $i$, andthe market index, $M$, follows a power-law distribution, $<\rho_{iM}(k) > \simk^{\gamma}$, with the exponent $\gamma_{\textrm{S&P500}} \approx 0.16$ and$\gamma_{\textrm{KOSPI}} \approx 0.14$, respectively. Thus, regardless of themarkets, the indivisual stocks closely related to the common factor in themarket, the market index, are likely to be located around the center of thenetwork between stocks, while those weakly related to the market index arelikely to be placed in the outside

Topological Properties of a Minimal Spanning Tree in the Korean and the American Stock Markets