Calculator
Example Data Table
| Input Line | Meaning | Effect |
|---|---|---|
| A,B | Edge between A and B | Adds one degree to A and B. |
| C,D | Edge between C and D | Adds one degree to C and D. |
| D,D | Loop at D | Adds two to D when loops are enabled. |
| E,F,2 | Weighted edge | Adds two when weighted mode is enabled. |
Formula Used
Undirected degree: d(v) is the number of edges incident to node v.
Loop rule: a self loop contributes 2 to undirected degree when loop counting is enabled.
Directed degree: d(v) = in degree(v) + out degree(v).
Weighted degree: replace each edge count with its weight. This is also called node strength.
Normalized degree: d(v) / (r - 1) for undirected networks.
Directed normalized total: d(v) / (2 × (r - 1)) when total in and out degree are combined.
Density: actual non-loop edge lines divided by possible non-loop edge pairs.
How to Use This Calculator
- Enter one edge per line in the edge list box.
- Use source,target,weight when weighted mode is needed.
- Add isolated nodes in the node list box.
- Select directed or undirected network type.
- Choose delimiter, loop, weight, and normalization options.
- Enter a focus node when you want one highlighted result.
- Press Calculate Degree to view the result above the form.
- Use CSV or PDF buttons to download the current calculation.
Understanding Node Degree
Node degree is a first check for any network. It counts how many links touch each node. In an undirected graph, each normal edge adds one count to both endpoints. A loop can add two counts when that option is enabled. In a directed graph, the calculator separates incoming links and outgoing links. Their sum gives the total degree.
Why the Value Matters
Degree helps you find busy nodes, weak nodes, and possible bridge points. A high degree can mean a hub. A low degree can mean a leaf, an isolated item, or a missed record. Weighted mode changes the count into strength. Then each edge contributes its numeric weight instead of one. This is useful for traffic, collaboration, cost, contact, or flow networks.
Network Order R
The calculator uses r as the number of nodes in the network. It collects nodes from the edge list and the optional node list. You may also enter an override for r when you want a fixed normalization base. Normalized degree divides a node value by the largest possible value for that mode. This makes small and large networks easier to compare.
Good Data Practice
Use one edge per line. Write source and target nodes first. Add weight as the third value when weighted mode is active. Keep names consistent. For example, A and a are treated as different nodes. Add isolated nodes in the node box, because they have no edge line. This keeps r correct and shows zero degree rows.
Interpreting Results
The result table shows each node with in degree, out degree, total degree, and normalized value. For undirected networks, in and out values are shown as zero, because edge direction is not used. The summary shows average degree, maximum nodes, density, and valid edge count. Export the result when you need a record for reports, audits, teaching, or graph review. Use the focus node field for a quick single node check. The full table still appears, so context is not lost. Review warnings before trusting totals. They show skipped lines, invalid weights, or missing endpoints. Clean inputs give clearer centrality comparisons and better downloadable files for later analysis. Share settings with teammates so results stay reproducible.
FAQs
What is node degree?
Node degree is the number of links connected to a node. In directed networks, it can be split into in degree and out degree.
What does r mean?
Here, r means the total number of nodes used as the network order. It is used for normalized degree calculations.
How are loops counted?
For undirected networks, a loop can add two to the node degree. You can turn loop counting off in the form.
What is weighted degree?
Weighted degree adds edge weights instead of counting every edge as one. It is useful when links have strength, cost, flow, or frequency.
Can I calculate directed degree?
Yes. Select directed network type. The result table will show in degree, out degree, total degree, and normalized total degree.
Why add isolated nodes?
Isolated nodes have no edge line. Adding them keeps r correct and shows zero degree values in the final table.
What is normalized degree?
Normalized degree divides a node degree by the maximum possible degree. It helps compare nodes across networks of different sizes.
Can I download the result?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple report copy of the calculated results.