Adjacency Matrix Converter
Convert a graph between an edge list, an adjacency matrix, and an incidence matrix — directed or undirected, weighted or not. Runs entirely in your browser, no server, no sign-up.
What this tool does
Convert a graph between the three ways people usually write one down — an edge list, an adjacency matrix, and an incidence matrix. Pick the Input format your data is in and the Output format you want, set Directed and Weighted to match your graph, and the conversion runs instantly. Nothing is sent to a server — it works locally, offline, and needs no sign-up.
The three representations
| Representation | What it looks like | Good for |
|---|---|---|
| Edge list | One edge per line: A B (or A B 3 when weighted) | Writing a graph by hand, sparse graphs |
| Adjacency matrix | A square n×n table; cell (i, j) is the edge from i to j | Algorithms, dense graphs, linear algebra |
| Incidence matrix | A vertices × edges table; one column per edge | Flow problems, graph Laplacian, circuit analysis |
Input format
- edges (default) — one edge per line. Endpoints are separated by a space or
a comma (
A BorA,B). Add a third token for the weight (A B 3) when Weighted is on. A line with a single token (D) declares an isolated vertex. Lines starting with#are comments and are ignored. - adjacency — a square numeric matrix, one row per line, cells separated by
spaces or commas. A header row and/or a leading label column are detected
automatically; without them, vertices are named
V1, V2, ….
Output format
- adjacency (default) — a labelled square adjacency matrix (tab-separated, with a label row and column).
- incidence — a vertices × edges matrix, one column per edge (
e1, e2, …). For an undirected graph an endpoint cell holds the edge weight (a self-loop is2×weight). For a directed graph the tail is-weightand the head is+weight. - edges — a normalized edge list (handy for cleaning up or de-duplicating a hand-written one, or extracting edges out of a matrix).
- list — an adjacency list, one line per vertex (
A: B C); weighted neighbours show asB(3). - degree — the diagonal degree matrix
D, each vertex's (weighted) degree on the diagonal. - laplacian — the graph Laplacian
L = D − A(undirected graphs only), used for spectral graph theory and the number of spanning trees.
Directed and weighted
- Directed — when on,
A Bis a one-way edge and does not implyB A. When off (the default) the graph is undirected and the adjacency matrix is symmetric. - Weighted — when on, edge weights are read (the 3rd token of an edge line,
or the value of a matrix cell) and emitted. When off, every present edge is
1.
Examples
| Input | From → To | Settings | Output |
|---|---|---|---|
A B / B C / A C | edges → adjacency | undirected | a symmetric 3×3 matrix for the triangle |
A B / B C | edges → adjacency | directed | upper-triangular (A→B, B→C only) |
A B 5 / B C 2.5 | edges → adjacency | weighted | cells carry 5 and 2.5 |
| a labelled matrix | adjacency → edges | — | the edge list it represents |
A B / B C | edges → incidence | undirected | columns e1, e2, two 1s per column |
FAQ
Is it free and private?
Yes — your graph never leaves your device, and the tool keeps working offline once the page has loaded.
How are matrices laid out?
Tab-separated, with the vertex labels in the first row and first column so you can paste the result straight into a spreadsheet.
What sign convention does the directed incidence matrix use?
The edge's tail
(source) is -1 (or -weight) and its head (target) is +1 (or +weight),
matching the standard oriented incidence matrix used for the graph Laplacian.
Can I round-trip?
Yes — convert edges → adjacency → edges and you get the same graph back. Isolated vertices survive because they are written as a single-token line in the edge-list output.
Developer & Automation Access
Run it from the terminal
Same engine as this page, headless — via the gizza CLI:
gizza tool adjacency-matrix-converter "A B
B C
A C"New to the CLI? Get gizza →
Open it by URL
Pre-fill and auto-run this tool with query parameters — the names match the API/CLI:
https://gizza.ai/tools/adjacency-matrix-converter/?input=A%20B%0AB%20C%0AA%20C&from=auto&to=adjacency&directed=true&weighted=true&power=2Machine-readable descriptor: tool.json — title + parameters JSON Schema for agents.