  We confirm a conjecture by Everett, Sinclair, and Dankelmann~[Some Centrality
results new and old, J. Math. Sociology 28 (2004), 215--227] regarding the
problem of maximizing closeness centralization in two-mode data, where the
number of data of each type is fixed. Intuitively, our result states that among
all networks obtainable via two-mode data, the largest closeness is achieved by
simply locally maximizing the closeness of a node. Mathematically, our study
concerns bipartite graphs with fixed size bipartitions, and we show that the
extremal configuration is a rooted tree of depth~$2$, where neighbors of the
root have an equal or almost equal number of children.
