# Coordination Number

From Soft-Matter

### Definition

The number of touching neighbors per particle in a granular material.^{1}

### Discussion

Often, the value of interest is the average coordination number, <math>\langle z \rangle</math>. If <math>n_z\,</math> is the number of rods with <math>z\,</math> touching neighbors, then we can calculate <math>\langle z \rangle</math> as a weighted average.

<math>\langle z \rangle = \frac{\sum_z z n_z}{\sum_z n_z} \equiv \sum_z z \gamma_z </math>,

where <math>\gamma_z \equiv \frac{n_z}{\sum_z n_z}</math> is defined as the coordination number distribution function. <math>\gamma_z\,</math> will depend on the shape of the grains.

### References

^{1}J. Blouwolff and S. Fraden. "The coordination number of granular cylinders." *Europhys. Letters*, **76** (6), pp. 1095-1101 (2006).