Create directed or undirected incidence matrices with instant validation. Visualize vertex degrees and edge patterns. Download tables for classes, assignments, audits, or research.
This calculator converts an edge list into an incidence matrix, validates graph inputs, summarizes vertex incidence, and plots degree-style totals for quick interpretation.
Enter graph settings below. Use one edge per line. For weighted mode, enter: from to weight.
This sample shows a directed graph edge list and the kind of source data the calculator accepts.
| Edge | From Vertex | To Vertex | Weight | Meaning |
|---|---|---|---|---|
| e1 | 1 | 2 | 1 | Edge leaves 1 and enters 2 |
| e2 | 1 | 3 | 1 | Edge leaves 1 and enters 3 |
| e3 | 2 | 4 | 1 | Edge leaves 2 and enters 4 |
| e4 | 3 | 4 | 1 | Edge leaves 3 and enters 4 |
| e5 | 4 | 5 | 1 | Edge leaves 4 and enters 5 |
For a graph with vertices as rows and edges as columns, the incidence matrix entry is based on how a vertex touches an edge.
Directed graph: If edge e goes from vertex u to vertex v, then for column e: row u = -w, row v = +w, and all other rows = 0.
Undirected graph: If edge e connects vertices u and v, then for column e: row u = w, row v = w, and all other rows = 0.
Self-loop: In undirected mode, a self-loop may be represented with 2w at the same vertex row.
Here, w is the edge weight. In unweighted graphs, the calculator uses w = 1.
An incidence matrix represents how graph vertices connect to edges. Rows usually represent vertices, columns represent edges, and each entry shows whether a vertex participates in an edge.
Directed mode places a negative value at the source vertex row and a positive value at the destination vertex row for each edge column. All other entries stay zero.
Undirected mode marks both incident vertices positively for the same edge. This highlights connection membership without assigning travel direction between the two endpoints.
Yes. Enable weighted mode and enter each edge as three values: start vertex, end vertex, and weight. Those weights are used directly in the matrix entries.
The calculator validates every line. If an edge references a vertex below 1 or above the declared vertex count, it shows a clear error message.
This layout helps you see the final matrix immediately after submission while keeping the form available below for quick corrections and repeated testing.
The chart displays total incidence by vertex. In directed graphs, the summary table also shows separate incoming and outgoing totals for deeper analysis.
Click the PDF button. It opens the browser print flow, where you can save the formatted result section and page content as a PDF document.
Incidence matrices are useful in graph theory, network design, circuit analysis, flow models, scheduling, discrete mathematics, and algorithm education. This page combines validation, matrix generation, export tools, and a quick visual summary in one interface.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.