  It is well-known that the behavior of many dynamical processes running on
networks is intimately related to the eigenvalue spectrum of the network. In
this paper, we address the problem of inferring global information regarding
the eigenvalue spectrum of a network from a set of local samples of its
structure. In particular, we find explicit relationships between the so-called
spectral moments of a graph and the presence of certain small subgraphs, also
called motifs, in the network. Since the eigenvalues of the network have a
direct influence on the network dynamical behavior, our result builds a bridge
between local network measurements (i.e., the presence of small subgraphs) and
global dynamical behavior (via the spectral moments). Furthermore, based on our
result, we propose a novel decentralized scheme to compute the spectral moments
of a network by aggregating local measurements of the network topology. Our
final objective is to understand the relationships between the behavior of
dynamical processes taking place in a large-scale complex network and its local
topological properties.
