  Observability and estimation are closely tied to the system structure, which
can be visualized as a system graph--a graph that captures the
inter-dependencies within the state variables. For example, in social system
graphs such inter-dependencies represent the social interactions of different
individuals. It was recently shown that contractions, a key concept from graph
theory, in the system graph are critical to system observability, as (at least)
one state measurement in every contraction is necessary for observability.
Thus, the size and number of contractions are critical in recovering for loss
of observability. In this paper, the correlation between the
average-size/number of contractions and the global clustering coefficient (GCC)
of the system graph is studied. Our empirical results show that estimating
systems with high GCC requires fewer measurements, and in case of measurement
failure, there are fewer possible options to find substitute measurement that
recovers the system's observability. This is significant as by tuning the GCC,
we can improve the observability properties of large-scale engineered networks,
such as social networks and smart grid.
