# Degree centrality

> Degree centrality is the number of ties a person has. The formula, the normalised version, in-degree and out-degree, and a worked example on Krackhardt's kite.

Source: https://netgraf.isik.co/learn/degree-centrality
Updated: 2026-09-24

Degree centrality is the number of ties a person has. It is the simplest measure of centrality: in a network of who talks to whom, the person with the highest degree talks to the most people. Divided by the number of other people in the network, it becomes a share between 0 and 1.

## How it's calculated

```
degree(v)            = number of ties touching v
normalised degree(v) = degree(v) / (n - 1)
```

n is the number of people. The normalised form lets you compare people across networks of different sizes.

When ties have a direction, degree splits in two. **In-degree** counts ties pointing at a person (how often they are chosen, cited or asked for help). **Out-degree** counts ties pointing away (how often they choose, cite or ask). In a classroom [sociogram](https://netgraf.isik.co/learn/sociogram), in-degree is popularity.

## What it tells you, and what it misses

Degree is a good first measure of activity, visibility and popularity, and it is the only centrality measure that needs nothing beyond each person's own ties. It says nothing about where those ties lead. In Krackhardt's kite, Diane has the most ties of anyone, but every one of them runs into the same busy cluster; she is not the person holding the network together. That is [betweenness](https://netgraf.isik.co/learn/betweenness-centrality).

## In Netgraf

Degree is the default size of each dot in the Graph view, and the Insights panel lists the most connected people first, under **Most connected**. The distribution chart in the panel shows how many people have each number of ties, which is where a hub-and-spoke network gives itself away.

## Questions

### Is higher degree centrality always better?

No. High degree means many direct ties, which brings visibility but also demands. A person with fewer ties that bridge separate groups can be more influential. Read degree alongside betweenness and closeness.

### What is the difference between degree and weighted degree?

Degree counts ties. Weighted degree, also called strength, adds up the weights on those ties, such as the number of emails or meetings. Two people with five ties each can have very different strength.

## Example maps

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

## References

- Freeman, L. C. (1978). Centrality in social networks: Conceptual clarification. Social Networks, 1(3), 215-239. https://doi.org/10.1016/0378-8733(78)90021-7
- Krackhardt, D. (1990). Assessing the political landscape: Structure, cognition, and power in organizations. Administrative Science Quarterly, 35(2), 342-369. https://doi.org/10.2307/2393394