PageRank Calculator
Use short node labels. Enter one edge per line as from,to,weight. Weight is optional and defaults to 1.
Example Data Table
This example matches the default graph loaded in the form.
| From Node | To Node | Weight | Meaning |
|---|---|---|---|
| A | B | 1 | A links once to B. |
| A | C | 1 | A links once to C. |
| B | C | 1 | B links once to C. |
| B | D | 1 | B links once to D. |
| C | A | 1 | C links once to A. |
| C | B | 1 | C links once to B. |
| C | D | 1 | C links once to D. |
| D | C | 1 | D links once to C. |
| E | C | 1 | E links once to C. |
| E | D | 1 | E links once to D. |
Formula Used
This calculator uses the weighted PageRank update rule for directed graphs:
PRk+1(i) = (1 − d)vi + d × Σ [ PRk(j) × wji / OutWeight(j) ] + d × DanglingMass × vi
- d is the damping factor, usually 0.85.
- vi is the personalization probability for node i.
- wji is the edge weight from node j to node i.
- OutWeight(j) is the total outgoing weight from node j.
- DanglingMass is the rank from nodes with no outbound links.
Iteration continues until the L1 difference between successive rank vectors falls below the tolerance, or the maximum iteration limit is reached.
How to Use This Calculator
- Enter node labels in the node list, or let edges define them automatically.
- Add one directed edge per line using from,to,weight.
- Set the damping factor, tolerance, and maximum iterations.
- Optionally enter a personalization vector for biased rank distribution.
- Choose the initial rank mode.
- Click Calculate PageRank.
- Review the ranked nodes, convergence table, and Plotly graphs.
- Download the results as CSV or PDF.
FAQs
1. What does PageRank measure?
PageRank estimates how important a node is within a directed network. A node receives higher rank when important nodes link to it, especially through concentrated outbound weight.
2. Why is the damping factor important?
The damping factor controls how often a random surfer follows links versus jumps elsewhere. Values near 0.85 are standard because they balance structure awareness and numerical stability.
3. What are dangling nodes?
Dangling nodes have no outgoing links. Their rank cannot flow through normal transitions, so this calculator redistributes that mass using the personalization vector.
4. Can I use weighted links?
Yes. Larger weights increase the fraction of rank passed along that edge. If weights are omitted, every link uses weight 1 by default.
5. What does personalization do?
Personalization biases teleportation and dangling redistribution toward selected nodes. It is useful for topic-sensitive ranking, recommendation systems, and custom authority analysis.
6. Why might the calculator not converge quickly?
Slow convergence often appears in larger graphs, strict tolerances, or structures with tight cycles. Increasing the iteration limit usually resolves the issue.
7. Do scores always sum to one?
Yes, aside from minor floating-point rounding. The iterative process keeps the probability mass normalized across all nodes in the network.
8. How should I read the graphs?
The bar chart compares final node importance. The convergence chart shows how fast the solution stabilized by tracking the L1 delta across iterations.