  In this study, we have investigated factors of determination which can affect
the connected structure of a stock network. The representative index for
topological properties of a stock network is the number of links with other
stocks. We used the multi-factor model, extensively acknowledged in financial
literature. In the multi-factor model, common factors act as independent
variables while returns of individual stocks act as dependent variables. We
calculated the coefficient of determination, which represents the measurement
value of the degree in which dependent variables are explained by independent
variables. Therefore, we investigated the relationship between the number of
links in the stock network and the coefficient of determination in the
multi-factor model. We used individual stocks traded on the market indices of
Korea, Japan, Canada, Italy and the UK. The results are as follows. We found
that the mean coefficient of determination of stocks with a large number of
links have higher values than those with a small number of links with other
stocks. These results suggest that common factors are significantly
deterministic factors to be taken into account when making a stock network.
Furthermore, stocks with a large number of links to other stocks can be more
affected by common factors.
