We investigate whether herd behavior in equity market is led by ‘core’ stocks or by ‘peripheral’ stocks connected to core stocks, which we identify using the minimum spanning tree, a technique in network theory. Using non-securities stocks listed in the Korea Exchange from January 2005 to December 2015, we find that core stocks are not necessarily the stocks whose market values are large but are mid-sized stocks. As in previous studies, we find strong evidence of herding in the Korean stock market. However, herding arises only when the market is in stress: during bear states, core stocks herd toward to the market return and peripheral stocks herd to core stocks in their clusters. During bull markets, however, adverse herding arises mainly driven by securities stocks and thus cross-sectional dispersion in returns increases.