In status competition studies, the utility of heterogeneous individuals typically depends on an economy-wide average indicator of status. In our model, emulative and jealous agents are embedded in an exogenous network where agent-specific reference group is determined by the direct link emanating from the agent. Similarly to Ghiglino and Goyal (2010) but in a somewhat different framework, we show that individual consumption is proportional to the agent's “outbound” Katz-Bonacich network centrality measure and equilibrium is generally inefficient. More important, the negative externality associated with each agent depends on her “inbound” centrality measure—the conspicuousness index. A tax based on this index combined with a uniform lump-sum transfer attains efficiency.