  We investigate a factor that can affect the number of links of a specific
stock 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. Among
the common factors mentioned in the arbitrage pricing model (APM), widely
acknowledged in the financial field, a representative market index is
established as a possible factor. We found that the correlation distribution,
$\rho_{ij}$, of 400 stocks taken from the S&P500 index shows a very similar
with that of the Korean stock market and those deviate from the correlation
distribution of time series removed a nonlinearity by the surrogate method. We
also shows that the degree distribution of the MSTs for both stock markets
follows a power-law distribution with the exponent $\zeta \sim$ 2.1, while the
degree distribution of the time series eliminated a nonlinearity follows an
exponential distribution with the exponent, $\delta \sim 0.77$. Furthermore the
correlation, $\rho_{iM}$, between the degree k of individual stock, $i$, and
the market index, $M$, follows a power-law distribution, $<\rho_{iM}(k) > \sim
k^{\gamma}$, with the exponent $\gamma_{\textrm{S&P500}} \approx 0.16$ and
$\gamma_{\textrm{KOSPI}} \approx 0.14$, respectively. Thus, regardless of the
markets, the indivisual stocks closely related to the common factor in the
market, the market index, are likely to be located around the center of the
network between stocks, while those weakly related to the market index are
likely to be placed in the outside.
