What is an adjacency matrix?

It's a square grid where rows and columns both represent the graph's nodes, and entry (i, j) contains the weight of the edge from node i to node j (or 0 if none exists).

Why is the matrix symmetric?

Because this calculator treats every edge as undirected, an edge between A and B affects both entry (A, B) and entry (B, A) equally, making the matrix symmetric across its diagonal.

What does the degree sequence mean?

A node's degree is the number of edges connected to it — the degree sequence lists this count for every node, a useful summary statistic checked by tools like the site's Graph Degree Sequence Validator.

Can I build an unweighted adjacency matrix?

Yes — enter edges without a weight, like A-B, and the calculator treats each present edge as weight 1, the standard convention for unweighted adjacency matrices.

What does a 0 in the matrix mean?

A 0 at entry (i, j) means there's no edge directly connecting node i and node j — it doesn't mean they're unreachable, just not directly connected.

How large a graph can this calculator handle?

This calculator supports up to 30 nodes, since the matrix grows as the square of the node count and stays comfortably readable at that size.

Why are the nodes listed in alphabetical order?

Sorting node labels alphabetically gives a consistent, predictable row and column order regardless of the order edges were entered in, making the matrix easier to read and compare across runs.

Where are adjacency matrices used in real life?

They're used throughout graph algorithms and network analysis (computing connectivity via matrix powers, spectral graph theory, and social network analysis), and are a standard way to feed graph structure into linear-algebra-based computations.

Adjacency Matrix Calculator — Convert an Edge List to a Matrix

Our Adjacency Matrix Calculator takes a graph entered as a simple text edge list (weighted like A-B:4 or unweighted like A-B) and builds its full adjacency matrix — a grid showing which nodes connect to which, and at what weight — along with the derived degree sequence for every node.

Quick Answer

Enter your graph as an edge list to instantly build its adjacency matrix and see the degree sequence for every node.

Edges (comma-separated)

Enter edges as NodeA-NodeB (unweighted) or NodeA-NodeB:weight (weighted), e.g. A-B, A-C:2.

How to Use the Adjacency Matrix Calculator — Build a Graph Matrix Online

1
Enter your graph as a comma-separated edge list, e.g. A-B, A-C, B-C (unweighted) or A-B:4, A-C:2 (weighted).
2
Click 'Calculate' to build the adjacency matrix.
3
Review the matrix grid and the degree of each node.

Why Use Adjacency Matrix Calculator — Build a Graph Matrix Online?

An adjacency matrix represents a graph as a grid of numbers: entry (i, j) holds the weight of the edge between node i and node j, or 0 if no edge exists — a representation that turns graph problems into matrix and linear algebra problems, and that many graph algorithms use internally for fast edge lookups. This calculator builds that matrix directly from a compact edge-list description and reads off the degree sequence (how many edges touch each node) as a byproduct.

Frequently Asked Questions

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