  In this paper we study the maximum degree of interaction which may emerge in
distributed systems. It is assumed that a distributed system is represented by
a graph of nodes interacting over edges. Each node has some amount of data. The
intensity of interaction over an edge is proportional to the product of the
amounts of data in each node at either end of the edge. The maximum sum of
interactions over the edges is searched for. This model can be extended to
other interacting entities. For bipartite graphs and odd-length cycles we prove
that the greatest degree of interaction emerge when the whole data is
concentrated in an arbitrary pair of neighbors. Equal partitioning of the load
is shown to be optimum for complete graphs. Finally, we show that in general
graphs for maximum interaction the data should be distributed equally between
the nodes of the largest clique in the graph. We also present in this context a
result of Motzkin and Straus from 1965 for the maximal interaction objective.
