---
tag: CWPRX0R5ET
kind: concept
name: Coordination sequence
sources:
  - wikipedia: en:67980941@r1376023393
    locator: Coordination sequence
    note: adopted
    mention: wikipedia://en/67980941
    sections: [Summary]
same_as:
  wikidata: Q107394824
  wikipedia: Coordination sequence
inventory: [2JM6MHSTR3]
---

## Summary

In crystallography and graph theory, the **coordination sequence** of a vertex $v$ is an integer sequence that counts how many vertices are at each possible [[distance|0QV9VNNB4Z]] from $v$. That is, it is a sequence

$$n_0, n_1, n_2,\dots$$

where each $n_i$ is the number of vertices that are $i$ steps away from $v$. If the graph is vertex-transitive, then the sequence is an invariant of the graph that does not depend on the specific choice of $v$. Coordination sequences can also be defined for sphere packings, by using either the contact graph of the spheres or the Delaunay triangulation of their centers, but these two choices may give rise to different sequences.