What is an adjacency matrix?

An adjacency matrix is an N×N grid where entry (i, j) is 1 if there is an edge from node i to node j, and 0 otherwise. It is one of the two standard ways to represent a graph (the other being an adjacency list).

How are directed and undirected graphs different in the matrix?

For undirected graphs the matrix is symmetric: if (i,j) is 1 then (j,i) is also 1. For directed graphs, (i,j) and (j,i) are set independently based on which directed edges you entered.

What does the degree sequence show?

For undirected graphs, the degree of a node is the number of edges connected to it. For directed graphs, in-degree and out-degree are listed separately. The sequence is sorted in non-increasing order.

Can nodes have self-loops?

Yes. Enter an edge where both endpoints are the same label (e.g. "A A") and the diagonal entry for that node will be set to 1.

How many nodes and edges are supported?

The tool handles graphs up to 26 nodes comfortably in the browser. Very large graphs may make the matrix hard to read, but there is no hard limit.

Adjacency Matrix Tool

Name: Adjacency Matrix Tool
Availability: InStock
Author: Nham Vu

Enter graph edges and instantly see the adjacency matrix, degree sequence, and basic graph properties.

Graph Input

Graph Type

Undirected Directed

Edge List (one edge per line, e.g. A B)

Enter edges on the left and click Build Matrix.

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Summary

Enter graph edges and instantly see the adjacency matrix, degree sequence, and basic graph properties.

How it works

Choose directed or undirected graph mode.
Enter edges one per line using the format "A B" or "1 2" (two node labels separated by a space).
Click Build Matrix to generate the adjacency matrix.
Read the N×N grid — a 1 means an edge exists between row-node and column-node.
Check the degree sequence and statistics table below the matrix.

Use cases

Verify hand-built adjacency matrices for graph theory homework.
Quickly visualize small graphs for algorithm design or debugging.
Check degree sequences before applying degree-based theorems.
Understand directed vs. undirected edge representation side-by-side.
Prepare data for graph algorithms that require matrix input.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu

Adjacency Matrix Tool

Graph Input