  In this paper, we propose a novel approach that employs kinetic equations to
describe the collective dynamics emerging from graph-mediated pairwise
interactions in multi-agent systems. We formally show that for large graphs and
specific classes of interactions a statistical description of the graph
topology, given in terms of the degree distribution embedded in a
Boltzmann-type kinetic equation, is sufficient to capture the collective trends
of networked interacting systems. This proves the validity of a commonly
accepted heuristic assumption in statistically structured graph models, namely
that the so-called connectivity of the agents is the only relevant parameter to
be retained in a statistical description of the graph topology. Then we
validate our results by testing them numerically against real social network
data.
