  We introduce a network growth model based on complete redirection: a new node
randomly selects an existing target node, but attaches to a random neighbor of
this target. For undirected networks, this simple growth rule generates
unusual, highly modular networks. Individual network realizations typically
contain multiple macrohubs---nodes whose degree scales linearly with the number
of nodes $N$. The size of the network "nucleus"---the set of nodes of degree
greater than one---grows sublinearly with $N$ and thus constitutes a
vanishingly small fraction of the network. The network therefore consists
almost entirely of leaves (nodes of degree one) as $N\to\infty$.
