We examine from an economic view the possible factors that can affect the number of links with other stocks in a stock network by a cross-correlation-based method, a minimal spanning tree(MST), using individual stocks in American($S&P$500) and Korean(KOSPI) stock markets. Among the well known common factors in the financial field, the market index has been identified as a possible one. We have found a power-law behavior in topological properties of the stock network where the degree distribution obtained through the cross-correlation-based MST method exhibits a power-law with an exponent $\zeta \sim$ 2.1, for all stock markets explored. Furthermore, in a degree distribution, the relationship between the number of links with other stocks and the correlation between the market index and individual stocks follows a power-law distribution. This suggests that the number of links with other stocks is significantly affected by the market index. That is, the stocks with a large number of links in a stock network are more strongly correlated with the market index than those with a small number of links.
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