Enter adjacency matrix
Use rows on new lines. Separate entries using spaces or commas. Values may be weighted. The matrix must be square (n×n).
Example data table
This example uses a small weighted adjacency matrix. Paste the matrix above, then compare the ranked centrality scores.
| Node | Connections (weights) | Interpretation |
|---|---|---|
| A | A→B=1, A→C=1 | A influences B and C equally. |
| B | B→A=1, B→C=1 | B links to two strong neighbors. |
| C | C→A=1, C→B=1, C→D=1 | C sits near the network core. |
| D | D→C=1 | D depends on C for influence. |
Formula used
Eigenvector centrality assigns each node a score proportional to the scores of its neighbors. For an adjacency matrix A, the centrality vector x satisfies:
This calculator uses power iteration: it repeatedly multiplies a trial vector by the selected operator (A or Aᵀ), then normalizes, until the change drops below the tolerance.
How to use this calculator
- Enter a square adjacency matrix using spaces or commas.
- Choose directed or undirected mode as needed.
- Select in-centrality to emphasize incoming links.
- Set iteration controls and tolerance for precision.
- Click Calculate to view ranked centrality values.
- Use CSV or PDF buttons to export the table.
Notes for physics networks
Eigenvector centrality is common in interaction graphs: oscillator coupling, transport pathways, correlation networks, and connectivity in lattice models. It highlights nodes connected to other influential nodes, not just high-degree nodes.
- Weighted entries can represent coupling strength or transition rate.
- For asymmetric systems, compare in vs out centrality.
- Use ε regularization if the matrix is sparse and disconnected.