# Clustering coefficient

> The clustering coefficient measures how many of a person's contacts know each other. Local and global clustering, the formula, and a worked example.

Source: https://netgraf.isik.co/learn/clustering-coefficient
Updated: 2026-09-24

The clustering coefficient measures how many of a person's contacts are also tied to each other. A value of 1 means all of their contacts know one another; 0 means none do. Averaged or totalled across the network, it shows how cliquish the group is.

## How it's calculated

```
local clustering(v) = ties among v's neighbours / (k (k - 1) / 2)
transitivity        = 3 * triangles / connected triples
```

k is v's degree. Transitivity, the global form, is the share of two-step paths that are closed into triangles.

## What it tells you

High local clustering means a person sits inside a tight group where everyone knows everyone: good for trust and support, weak for new information. Low clustering with high degree is the signature of a [broker](https://netgraf.isik.co/learn/brokers-and-bridges). Watts and Strogatz showed in 1998 that most real networks combine high clustering with short paths, the "small world" pattern.

In Krackhardt's kite, Carol and Ed have the maximum local clustering of 1: all of their contacts are tied to each other. Ike, the only link between Jane and everyone else, has 0: his two contacts have never met.

## In Netgraf

The Insights panel's **How dense** card reports the global clustering coefficient (transitivity) alongside density.

## Questions

### What is the difference between transitivity and average clustering?

Transitivity counts closed triangles across the whole network at once, so high-degree people weigh more. Average clustering takes each person's local value and averages them, so everyone counts equally. They can differ a lot on the same network.

## Example maps

- https://netgraf.isik.co/m/krackhardt-kite

## References

- Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature, 393, 440-442. https://doi.org/10.1038/30918
- Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press.