# A simple algorithm for realizing a degree sequence as a connected graph

In Notes.

### Introduction

In graph theory, the *degree* of a vertex is the number of connections it has. For example, the vertices of the below graph have degrees (3, 2, 2, 1).

It is easy to determine the degrees of a graph’s vertices (i.e. its *degree sequence*), but what about the reverse problem? Given a list of integers, how can we construct a simple graph that has them as its vertex degrees? Does such a graph even exist? This blog post deals with a special case of this problem: **constructing connected simple graphs with a given degree sequence** using a simple and straightforward algorithm.

There are comments.