  The structural properties of suspensions and other multiphase systems are
vital to overall processability, functionality and acceptance among consumers.
Therefore, it is crucial to understand the intrinsic connection between the
microstructure of a material and the resulting rheological properties. Here, we
demonstrate how the transitions in the microstructural conformations can be
quantified and correlated to rheological measurements. We find semi-local
parameters from graph theory, the mathematical study of networks, to be useful
in linking structure and rheology. Our results, using capillary suspensions as
a model system, show that the use of the clustering coefficient, in combination
with the coordination number, is able to capture not only the agglomeration of
particles, but also measures the formation of groups. These phenomena are
tightly connected to the rheological properties. The present sparse networks
cannot be described by established techniques such as betweenness centrality.
