  We introduce a broad class of multi-hooking networks, wherein multiple copies
of a seed are hooked at each step at random locations, and the number of copies
follows a predetermined building sequence of numbers.
  We analyze the degree profile in random multi-hooking networks by tracking
two kinds of node degrees -- the local average degree of a specific node over
time and the global overall average degree in the graph. The former experiences
phases and the latter is invariant with respect to the type of building
sequence and is somewhat similar to the average degree in the initial seed. We
also discuss the expected number of nodes of the smallest degree.
  Additionally, we study distances in the network through the lens of the
average total path length, the average depth of a node, the eccentricity of a
node, and the diameter of the graph.
