How do you make an adjacency matrix?

List every node, draw an N×N grid with the nodes as row and column labels, then put a 1 (or the edge weight) in cell (i, j) for each edge from i to j and 0 elsewhere; in an undirected graph also fill (j, i). This maker does that automatically from edges typed as "A B", one per line.

What is an adjacency matrix?

An adjacency matrix is an N×N grid where entry (i, j) records the connection from node i to node j. This maker records edge counts in unweighted mode and summed weights in weighted mode.

How do I convert an adjacency matrix to an edge list?

Every non-zero cell (i, j) is an edge from node i to node j with that weight. For an undirected graph the matrix is symmetric, so read only the upper triangle including the diagonal to avoid listing each edge twice. Choose the Matrix input, paste the grid and the tool lists the edges.

How do I convert an adjacency list to an adjacency matrix?

For each line "A: B C", put a 1 in row A, columns B and C. In an undirected graph also set the mirror cells; if the list already shows both directions (A: B and B: A), the cell is set once, not doubled. Use "B(2.5)" for weighted neighbors.

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 or strength sequence show?

For unweighted graphs, degree counts incident edges; directed graphs show in-degree (column sum) and out-degree (row sum) separately. For weighted graphs, this tool reports strength—the sum of incident weights—instead. Values are sorted in non-increasing order.

What is graph density?

Density is the number of edges divided by the most possible: m ÷ (n(n−1)/2) for an undirected simple graph and m ÷ (n(n−1)) for a directed one. Self-loops are left out. The 4-node example with 4 edges has density 4 ÷ 6 = 0.667.

Can nodes have self-loops?

Yes. Enter an edge where both endpoints have the same label, such as A A. In an undirected graph, each self-loop contributes twice to that node’s degree.

How do I make a weighted adjacency matrix?

Enable Weighted, then enter source, target and weight on each line, such as A B 2.5. Parallel edge weights are added in the same matrix cell.

How do I include an isolated node?

Add its label to the optional Nodes field. It will appear with a zero row and zero column even when it has no edge.

Can I use this as a space adjacency matrix maker?

Yes, as a numeric matrix. Enter rooms or departments as nodes and each required relationship as an undirected edge, with Weighted on to score importance (for example 2 for must be adjacent, 1 for desirable). It outputs a square grid and adjacency list, not the triangular chart used in architectural programming.

Does this tool draw the graph?

Yes. Graphs with up to 40 nodes are drawn with the nodes on a circle, arrows for directed edges and weight labels when weighted. Larger graphs still get the matrix and lists.

How many nodes are supported?

The tool accepts up to 100 distinct nodes. Because an adjacency matrix contains N² cells, larger graphs are better represented with a sparse graph tool.

Adjacency Matrix Maker

Paste an edge list, an adjacency list or a matrix to get the adjacency matrix, adjacency list, edge list and a drawing of the graph, for directed, undirected, weighted or unweighted graphs, with degrees, density and components.

An adjacency matrix maker turns a list of edges into an N×N grid where row i, column j holds 1 (or the edge weight) when node i connects to node j, and 0 otherwise.

Graph Input

Graph Type

Undirected Directed

Weighted edges

Input Format

Nodes (optional; spaces or commas)

Edge List (one per line: A B)

Enter edges on the left and click Build.

Adjacency Matrix

Graph Drawing

Graph Properties

Adjacency List

Edge List

Degree Sequence

Matrix convention and privacy

Rows are sources and columns are targets. Parallel edges are summed, and an undirected self-loop appears once on the diagonal but contributes twice to unweighted degree. Weighted totals are labeled strength. Inputs are processed only in this browser and are not uploaded.

References: NetworkX adjacency matrix documentation and Wolfram AdjacencyMatrix documentation.

One Graph, Three Representations

Representation	Undirected A–B, A–C, B–C, C–D	Best for
Edge list	A B · A C · B C · C D	Input files, sparse graphs, weighted edges
Adjacency list	A: B C · B: A C · C: A B D · D: C	Traversal (BFS, DFS) in code; memory O(n + m)
Adjacency matrix	[[0,1,1,0],[1,0,1,0],[1,1,0,1],[0,0,1,0]]	Edge lookup in O(1), matrix powers (Aᵏ counts walks of length k); memory O(n²)

Conversions: edge list → matrix sets cell (u, v) for every edge (and (v, u) when undirected). Matrix → edge list reads every non-zero cell, using only the upper triangle for an undirected graph. Row sums are out-degrees and column sums are in-degrees. Density = m ÷ (n(n−1)/2) for undirected and m ÷ (n(n−1)) for directed simple graphs.

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Quick answer

An adjacency matrix maker turns a list of edges into an N×N grid where row i, column j holds 1 (or the edge weight) when node i connects to node j, and 0 otherwise. Undirected graphs give a symmetric matrix; directed graphs fill only source-to-target cells. Reading the non-zero cells back gives the edge list.

Example: Undirected edges A–B, A–C, B–C and C–D give rows A [0 1 1 0], B [1 0 1 0], C [1 1 0 1] and D [0 0 1 0], so the degrees are 2, 2, 3 and 1, there are 4 edges and the density is 4 ÷ 6 = 0.667.

Paste edges, an adjacency list or a matrix, then copy the result as CSV, LaTeX, Python or an edge list.

Summary

Enter edges as “A B” (or “A B 2.5” when weighted), an adjacency list as “A: B C”, or paste a square matrix, and this tool builds the N×N adjacency matrix, the adjacency list, the edge list and a circular drawing of the graph. An optional node list keeps isolated vertices. It reports degree or strength, edge count, density, connected components and self-loops, and exports CSV, LaTeX, Python or an edge list. Everything runs in your browser.

How it works

Choose the input format: edge list, adjacency list or matrix.
Choose directed or undirected and enable weights when needed.
Optionally enter every node to retain isolated vertices (or to name the rows of a pasted matrix).
Click Build to generate the adjacency matrix, adjacency list, edge list and graph drawing.
Read the N×N grid: each cell is an edge count or summed edge weight; rows are sources and columns are targets.
Check degree or strength, edge count, density and connected components, then export CSV, LaTeX, Python or the edge list.

Use cases

Verify hand-built adjacency matrices for graph theory homework.
Convert an adjacency matrix from a textbook back to an edge list or a picture of the graph.
Turn an adjacency list from code into a matrix for linear-algebra work.
Check degree sequences, density and connectivity before applying graph theorems.
Prepare data for NetworkX, MATLAB or other graph libraries.

Frequently Asked Questions

Last updated: 2026-10-09 · Reviewed by Nham Vu