We present a new index for measuring income inequality in networks. The index is based on income comparisons made by the members of a network who are linked with each other by direct social connections. To model the comparisons, we compose a measure of relative deprivation for networks. We base our new index on this measure. The index takes the form of a ratio: the network's aggregate level of relative deprivation divided by the aggregate level of the relative deprivation of a hypothetical network in which one member of the network receives all the income, and it is with this member that the other members of the network compare their incomes. We discuss the merits of this representation. We inquire how changes in the composition of a network affect the index. In addition, we show how the index accommodates specific network characteristics.