Random Graph Generator Calculator

Example Data Table

Formula Used

1) Maximum edges
For an undirected simple graph, the maximum possible edges are n(n−1)/2. For a directed graph without self-loops, the maximum is n(n−1).

2) Expected edges in G(n,p)
Expected edges = p × maximum possible edges.

3) Density
Density = actual edges / maximum possible edges.

4) Average degree
Average degree = sum of node degrees / number of nodes. In undirected graphs, this also equals 2E / n.

5) Clustering coefficient
For each node, local clustering = actual links among neighbors / possible neighbor links. The reported value is the mean across eligible nodes.

6) Average path length
Compute shortest paths between connected node pairs, then average those path distances. Disconnected pairs are excluded from the mean.

How to Use This Calculator

1. Select either the G(n,p) model or the G(n,m) model.
2. Enter the number of nodes you want in the graph.
3. For G(n,p), set the probability p. For G(n,m), set the target edge count m.
4. Choose whether the graph is directed and whether self-loops are allowed.
5. Pick a layout style for the plotted network.
6. Add an optional seed if you want repeatable random results.
7. Click Generate Random Graph to create the graph.
8. Review summary metrics, the Plotly network view, degree table, and edge list.
9. Use the CSV or PDF buttons to export the results.

FAQs

1) What does G(n,p) mean?

G(n,p) is a random graph model with n nodes. Each possible edge is independently included with probability p. It helps study expected connectivity and density patterns.

2) What does G(n,m) mean?

G(n,m) fixes the number of nodes and the exact number of edges. The calculator randomly selects m valid edges from all possible choices.

3) Why use a random seed?

A seed makes the random process repeatable. Using the same inputs and seed recreates the same graph, which is useful for testing and demonstrations.

4) What is graph density?

Density measures how full a graph is. It compares actual edges to the maximum possible edges allowed by the chosen graph rules.

5) Why can average path length show N/A?

If no connected node pairs exist beyond isolated nodes, there are no valid shortest paths to average. In that case, the result is not available.

6) Does degree mean incoming or outgoing links?

This calculator reports combined incident links for simplicity. In directed mode, it still summarizes total attached connections rather than separate in-degree and out-degree.

7) When should I use the circular layout?

Use the circular layout when you want a stable, clean arrangement for presentations. It is especially helpful when force layouts appear crowded.

8) Can I export the generated results?

Yes. The CSV export downloads the edge list and summary metrics. The PDF export captures the result section and graph for sharing or printing.