The Leverage of Weak Ties How Linking Groups Affects Inequality ∗

Centrality measures based on eigenvectors are important in models of how networks affect investment decisions, the transmission of information, and the provision of local public goods. We fully characterize how the centrality of each member of a society changes when initially disconnected groups begin interacting with each other via a new bridging link. Arbitrarily weak intergroup connections can have arbitrarily large effects on the distribution of centrality. For instance, if a high-centrality member of one group begins interacting symmetrically with a low-centrality member of another, the latter group has the larger centrality in the combined network in inverse proportion to the centrality of its emissary! We also find that agents who form the intergroup link, the “bridge agents”, become relatively more central within their own groups, while other intragroup centrality ratios remain unchanged.