  Random pure states of multi-partite quantum systems, associated with
arbitrary graphs, are investigated. Each vertex of the graph represents a
generic interaction between subsystems, described by a random unitary matrix
distributed according to the Haar measure, while each edge of the graph
represents a bi-partite, maximally entangled state. For any splitting of the
graph into two parts we consider the corresponding partition of the quantum
system and compute the average entropy of entanglement. First, in the special
case where the partition does not "cross" any vertex of the graph, we show that
the area law is satisfied exactly. In the general case, we show that the
entropy of entanglement obeys an area law on average, this time with a
correction term that depends on the topologies of the graph and of the
partition. The results obtained are applied to the problem of distribution of
quantum entanglement in a quantum network with prescribed topology.
