  We study the allocation of indivisible goods that form an undirected graph
and investigate the worst-case welfare loss when requiring that each agent must
receive a connected subgraph. Our focus is on both egalitarian and utilitarian
welfare. Specifically, we introduce the concept of egalitarian (resp.,
utilitarian) price of connectivity, which captures the worst-case ratio between
the optimal egalitarian (resp., utilitarian) welfare among all allocations and
that among the connected allocations. We provide tight or asymptotically tight
bounds on the price of connectivity for various large classes of graphs when
there are two agents as well as for paths, stars and cycles in the general
case. Many of our results are supplemented with algorithms which find connected
allocations with a welfare guarantee corresponding to the price of
connectivity.
