  Many physical systems are well modeled as collections of interacting
particles. Nevertheless, a general approach to quantifying the absolute degree
of order immediately surrounding a particle has yet to be described. Motivated
thus, we introduce a quantity $E$ that captures the amount of pairwise
informational redundancy among the bonds formed by a particle. Particles with
larger $E$ have less diversity in bond angles and thus simpler neighborhoods.
We show that $E$ possesses a number of intuitive mathematical properties, such
as increasing monotonicity in the coordination number of Platonic polyhedral
geometries. We demonstrate analytically that $E$ is, in principle, able to
distinguish a wide range of structures and conjecture that it is maximized by
the icosahedral geometry under the constraint of equal sphere packing. An
algorithm for computing $E$ is described and is applied to the structural
characterization of crystals and glasses. The findings of this study are
generally consistent with existing knowledge on the structure of such systems.
We compare $E$ to the Steinhardt order parameter $Q_6$ and polyhedral template
matching (PTM). We observe that $E$ has resolution comparable to $Q_6$ and
robustness similar to PTM despite being much simpler than the former and far
more informative than the latter.
