## 1. Introduction

In this tutorial, we’ll explain node degrees in a graph.

## 2. Node Degree

Let be a graph.

**The degree of a node is the number of edges with at one end.**

If the graph is simple, there can be no more than one edge between any two nodes. In that case, the degree of a node is equal to the number of its neighbors.

For example, the degree of is 4, and the degree of is 5 in this graph since they have 4 and 5 neighbors, respectively:

## 3. Directed Graphs

We differentiate between a node’s indegree and outdegree in a directed graph.

The indegree of a node is the number of edges whose target is . The outdegree of is analogously defined. It’s the number of edges whose source is .

In the example below, the indegree of is 3, and its outdegree is 1:

**The degree of a node is equal to the sum of its indegree and outdegree.** Only nodes in a directed graph have the indegree and outdegree.

## 4. Degree Distribution

**The degree distribution of a graph shows, for each possible degree , the fraction of nodes whose degree is .**

Let be the number of nodes whose degree is . The degree distribution is:

where is the total number of nodes in the graph.

This way, we get a probability distribution over natural numbers. We can use it to describe a graph or simulate graphs in numerical experiments.

For example, the distribution of the node degrees in the undirected graph above is:

## 5. Conclusion

In this article, we explained a node’s degree, indegree, and outdegree.

The degree of a node is the number of edges incident to it. In directed graphs, a node’s indegree is the number of edges directed into it, whereas its outdegree is the number of edges directed out of it.