gephi · natesteinmeyer · Aug 18, 2026
diff --git a/modules/WeightedBridgingCentrality/LICENSE.txt b/modules/WeightedBridgingCentrality/LICENSE.txt
diff --git a/modules/WeightedBridgingCentrality/README.md b/modules/WeightedBridgingCentrality/README.md
@@ -0,0 +1,151 @@
+# Weighted Bridging Centrality for Gephi
+
+Weighted Bridging Centrality is a Gephi plugin for calculating bridging centrality in weighted networks.
+
+The plugin extends the standard bridging-centrality calculation by allowing edge weights to represent connection strength. For shortest-path calculations, edge strength is converted to effective distance according to:
+
+d = 1 / w
+
+where `w` is the edge weight and `d` is the effective distance. Consequently, stronger connections are treated as shorter paths.
+
+The plugin calculates three node-level measures and adds them to the Gephi Data Laboratory:
+
+- **Weighted Betweenness Centrality**
+- **Bridging Coefficient**
+- **Weighted Bridging Centrality**
+
+Weighted Bridging Centrality is calculated as:
+
+Weighted Bridging Centrality = Weighted Betweenness Centrality × Bridging Coefficient
+
+## Origin and Attribution
+
+This plugin is an adaptation of the original **Bridging Centrality** plugin for Gephi. The original implementation is credited in the source code to Getúlio de Morais Pereira, Anderson Rodrigues dos Santos, and Luis Felipe Nunes Reis.
+
+The weighted adaptation was developed by **Nathan Steinmeyer**. It preserves the original plugin's bridging-coefficient calculation while modifying the betweenness-centrality calculation to support weighted shortest paths, interpreting edge weights as connection strengths through the transformation `d = 1/w`.
+
+The plugin has also been updated and packaged for the current Gephi plugin development environment.
+
+## Usage
+
+1. Install the plugin in Gephi.
+2. Import or create a weighted network.
+3. Ensure that the edge `Weight` values represent **connection strength**, where larger weights indicate stronger connections.
+4. Open the **Statistics** panel and run **Weighted Bridging Centrality**.
+5. Select whether the network should be treated as directed and whether the results should be normalized.
+6. After the calculation finishes, the following columns are added to the Data Laboratory:
+   - Weighted Betweenness Centrality
+   - Bridging Coefficient
+   - Weighted Bridging Centrality
+
+### Weight Interpretation
+
+This plugin assumes that edge weights represent **strength rather than distance**.
+
+For shortest-path calculations, each edge weight is transformed according to:
+
+`d = 1 / w`
+
+where:
+
+- `w` = edge weight (connection strength)
+- `d` = effective distance used for shortest-path calculations
+
+Therefore, a larger edge weight produces a shorter effective distance. For example, an edge with weight `10` has an effective distance of `0.1`, while an edge with weight `1` has an effective distance of `1`.
+
+Edge weights must be greater than zero.
+
+## Validation
+
+The weighted shortest-path implementation was manually validated against small networks with analytically determined results.
+
+### Four-Node Weighted Test
+
+Undirected network:
+
+| Edge | Weight |
+| --- | ---: |
+| A–B | 10 |
+| B–D | 10 |
+| A–C | 1 |
+| C–D | 1 |
+
+With normalization disabled, the expected and observed results were:
+
+| Node | Weighted Betweenness | Bridging Coefficient | Weighted Bridging Centrality |
+| --- | ---: | ---: | ---: |
+| A | 0.5 | 0.5 | 0.25 |
+| B | 1.0 | 0.5 | 0.50 |
+| C | 0.0 | 0.5 | 0.00 |
+| D | 0.5 | 0.5 | 0.25 |
+
+### Equal-Weight Shortest-Path Test
+
+The same four-node network was tested with all edge weights set to `1`. This creates multiple equally short paths and tests whether shortest-path contributions are divided correctly.
+
+All four nodes returned:
+
+- Weighted Betweenness Centrality: `0.5`
+- Bridging Coefficient: `0.5`
+- Weighted Bridging Centrality: `0.25`
+
+### Six-Node Weighted Test
+
+A more complex six-node network was also tested:
+
+| Edge | Weight |
+| --- | ---: |
+| A–B | 10 |
+| B–D | 10 |
+| A–C | 1 |
+| C–D | 1 |
+| B–E | 5 |
+| D–E | 5 |
+| C–F | 4 |
+| E–F | 2 |
+
+With normalization disabled, the plugin returned:
+
+| Node | Weighted Betweenness | Bridging Coefficient | Weighted Bridging Centrality |
+| --- | ---: | ---: | ---: |
+| A | 0 | 0.75 | 0 |
+| B | 3 | 0.2857 | 0.8571 |
+| C | 0 | 0.25 | 0 |
+| D | 0 | 0.3333 | 0 |
+| E | 5 | 0.2857 | 1.4286 |
+| F | 3 | 0.75 | 2.25 |
+
+These tests verify weighted shortest-path selection, handling of multiple equal shortest paths, calculation of the bridging coefficient, and calculation of Weighted Bridging Centrality.
+
+## References
+
+The calculations implemented in this plugin draw on the following algorithms and measures:
+
+- Brandes, Ulrik. 2001. “A Faster Algorithm for Betweenness Centrality.” *The Journal of Mathematical Sociology* 25 (2): 163–177. DOI: 10.1080/0022250X.2001.9990249.
+
+- Dijkstra, E. W. 1959. “A Note on Two Problems in Connexion with Graphs.” *Numerische Mathematik* 1: 269–271. DOI: 10.1007/BF01386390.
+
+- Hwang, Woochang, Taehyong Kim, Murali Ramanathan, and Aidong Zhang. 2008. “Bridging Centrality: Graph Mining from Element Level to Group Level.” In *Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining*, 336–344. DOI: 10.1145/1401890.1401934.
+
+Brandes provides the algorithmic basis for efficient betweenness-centrality calculation, including weighted networks. Dijkstra provides the shortest-path algorithm used for non-negative edge distances. Hwang et al. introduce the bridging coefficient and bridging-centrality measure on which the original Gephi plugin is based.
+
+## Requirements
+
+- Gephi 0.11.x
+- Java 17 or later
+
+## Building
+
+From the root of the `gephi-plugins` repository, run:
+
+`mvn clean package`
+
+The compiled `.nbm` plugin package will be generated under:
+
+`modules/WeightedBridgingCentrality/target/nbm/`
+
+## License
+
+This plugin is distributed under the GNU General Public License, version 3 (GPL-3.0). See `LICENSE.txt` for the full license text.
+
+This project is derived from the earlier Bridging Centrality plugin and retains attribution to its original contributors as described above.
diff --git a/modules/WeightedBridgingCentrality/pom.xml b/modules/WeightedBridgingCentrality/pom.xml
@@ -0,0 +1,94 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
+    <modelVersion>4.0.0</modelVersion>
+    <parent>
+        <artifactId>gephi-plugin-parent</artifactId>
+        <groupId>org.gephi</groupId>
+        <version>0.11.1</version>
+    </parent>
+
+    <groupId>com.nathansteinmeyer</groupId>
+    <artifactId>weighted-bridging-centrality</artifactId>
+    <version>1.0.0</version>
+    <packaging>nbm</packaging>
+
+    <name>Weighted Bridging Centrality</name>
+
+    <dependencies>
+            <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>statistics-api</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>graph-api</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>statistics-plugin</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>utils-longtask</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>ui-utils</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>utils</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.gephi</groupId>
+        <artifactId>core-library-wrapper</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.netbeans.api</groupId>
+        <artifactId>org-openide-util</artifactId>
+    </dependency>
+
+    <dependency>
+        <groupId>org.netbeans.api</groupId>
+        <artifactId>org-openide-util-lookup</artifactId>
+    </dependency>
+    </dependencies>
+
+    <build>
+        <plugins>
+            <plugin>
+                <groupId>org.apache.netbeans.utilities</groupId>
+                <artifactId>nbm-maven-plugin</artifactId>
+                <configuration>
+                    <licenseName>GPL-3.0</licenseName>
+                    <licenseFile>LICENSE.txt</licenseFile>
+                    <author>Nathan Steinmeyer</author>
+                    <publicPackages>
+                        <!-- Insert public packages -->
+                    </publicPackages>
+                </configuration>
+            </plugin>
+        </plugins>
+    </build>
+
+    <!-- Snapshot Repositories (only needed if developing against a SNAPSHOT version) -->
+    <repositories>
+        <repository>
+            <id>oss-sonatype</id>
+            <name>oss-sonatype</name>
+            <url>https://oss.sonatype.org/content/repositories/snapshots/</url>
+            <snapshots>
+                <enabled>true</enabled>
+            </snapshots>
+        </repository>
+    </repositories>
+</project>
+
+