## Katz Centrality

The plugin was developed under the initiative of the [Open University Of Israel](https://www.openu.ac.il/en/pages/default.aspx).

### The Algorithm Description

For a network with `n` nodes, the `n x n` adjacency matrix `A` is the matrix
in which `a_ij = 1` when the network has an edge from node `i` to node `j`; and
`a_ij = 0` otherwise. In the particular case in which the network is undirected
we have `a_ij = a_ji`; i.e. the adjacency matrix is symmetric `A = A^T`. More
generally, if the edges are weighted, then `a_ij` is the weight of the edge from
node `i` to node `j`:
The Katz (sometimes also called Katz-Bonacich) centrality measures with
the parameter of the network nodes are defined by the `n x 1` vector:


![Katz Centrality Formula](https://github.com/gephi/gephi-plugins/raw/katz-centrality-plugin/modules/KatzCentrality/KatzCentralityFormula.png)


### Installation

Open Gephi application, in the menu go to `Tools->Plugins->Available Plugins`. Click `Check for Newest` and search for `Katz Centrality` in the search text box. Select the checkbox and click `Install` and restart Gephi. The plugin should appear under `Node Overview` tab.

The plugin can also be installed manually:
- [Download](https://gephi.org/plugins/#/plugin/katz-centrality) the plugin.
- Open Gephi application.
- Go to Tools->Plugins menu, click on `Downloaded` tab, `Add Plugins` and select the plugin file, finally click `Install`. Restart the application.

After Gephi application re-opens the plugin will be available
under Node Overview plugins:

![Katz Centrality Plugin Location](https://github.com/gephi/gephi-plugins/raw/katz-centrality-plugin/modules/KatzCentrality/gephi_with_katz.png)

### Contributions

Any contributions to the plugin are welcome! Please note that currently there's an [issue](https://github.com/gephi/gephi/issues/1059) with Gephi development on Mac.