# Example Masked Triangle Count

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Many Graph operations can be performed using linear algebra and this connection is the subject of much recent research. EJML now has basic "Graph BLAS" capabilities as this example shows.

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## Example Code

```
/**
* Example using masked matrix multiplication to count the triangles in a graph.
* Triangle counting is used to detect communities in graphs and often used to analyse social graphs.
*
* More about the connection between graphs and linear algebra can be found at:
* https://github.com/GraphBLAS/GraphBLAS-Pointers.
*
* @author Florentin Doerre
*/
public class ExampleMaskedTriangleCount {
public static void main( String[] args ) {
// For the example we will be using the following graph:
// (0)--(1)--(2)--(0), (2)--(3)--(4)--(2), (5)
var adjacencyMatrix = new DMatrixSparseCSC(6, 6, 24);
adjacencyMatrix.set(0, 1, 1);
adjacencyMatrix.set(0, 2, 1);
adjacencyMatrix.set(1, 2, 1);
adjacencyMatrix.set(2, 3, 1);
adjacencyMatrix.set(2, 4, 1);
adjacencyMatrix.set(3, 4, 1);
// Triangle Count is defined over undirected graphs, therefore we make matrix symmetric (i.e. undirected)
adjacencyMatrix.copy().createCoordinateIterator().forEachRemaining(v -> adjacencyMatrix.set(v.col, v.row, v.value));
// In a graph context mxm computes all path of length 2 (a->b->c).
// But, for triangles we are only interested in the "closed" path which form a triangle (a->b->c->a).
// To avoid computing irrelevant paths, we can use the adjacency matrix as the mask, which assures (a->c) exists.
var mask = DMaskFactory.builder(adjacencyMatrix, true).build();
var triangleMatrix = CommonOpsWithSemiRing_DSCC.mult(adjacencyMatrix, adjacencyMatrix, null, DSemiRings.PLUS_TIMES, mask, null, null);
// To compute the triangles per vertex we calculate the sum per each row.
// For the correct count, we need to divide the count by 2 as each triangle was counted twice (a--b--c, and a--c--b)
var trianglesPerVertex = CommonOps_DSCC.reduceRowWise(triangleMatrix, 0, Double::sum, null);
CommonOps_DDRM.apply(trianglesPerVertex, v -> v/2);
System.out.println("Triangles including vertex 0 " + trianglesPerVertex.get(0));
System.out.println("Triangles including vertex 2 " + trianglesPerVertex.get(2));
System.out.println("Triangles including vertex 5 " + trianglesPerVertex.get(5));
// Note: To avoid counting each triangle twice, the lower triangle over the adjacency matrix can be used TRI<A> = A * L
}
}
```