Extend Graph Algorithms: Added Two Popular Algorithms: BronKerbosch, EdmondsKarp (#6576)

* Bron–Kerbosch algorithm added.

* test:Bron–Kerbosch algorithm added.

* lint checked.

* clang-format linting checked.

* lint checked in remote

Removed duplicate import statements for assertions.

* Remove unnecessary blank line in BronKerboschTest

* EdmondsKarp algorithm added.

* reformatted

---------

Co-authored-by: Oleksandr Klymenko <alexanderklmn@gmail.com>

src/test/java/com/thealgorithms/graph/BronKerboschTest.java

@@ -0,0 +1,79 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.ArrayList;
+import java.util.HashSet;
+import java.util.List;
+import java.util.Set;
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+class BronKerboschTest {
+
+    @Test
+    @DisplayName("Complete graph returns single clique")
+    void completeGraph() {
+        List<Set<Integer>> adjacency = buildGraph(4);
+        addUndirectedEdge(adjacency, 0, 1);
+        addUndirectedEdge(adjacency, 0, 2);
+        addUndirectedEdge(adjacency, 0, 3);
+        addUndirectedEdge(adjacency, 1, 2);
+        addUndirectedEdge(adjacency, 1, 3);
+        addUndirectedEdge(adjacency, 2, 3);
+
+        List<Set<Integer>> cliques = BronKerbosch.findMaximalCliques(adjacency);
+        assertEquals(1, cliques.size());
+        assertEquals(Set.of(0, 1, 2, 3), cliques.get(0));
+    }
+
+    @Test
+    @DisplayName("Path graph produces individual edges")
+    void pathGraph() {
+        List<Set<Integer>> adjacency = buildGraph(3);
+        addUndirectedEdge(adjacency, 0, 1);
+        addUndirectedEdge(adjacency, 1, 2);
+
+        List<Set<Integer>> cliques = BronKerbosch.findMaximalCliques(adjacency);
+        Set<Set<Integer>> result = new HashSet<>(cliques);
+        Set<Set<Integer>> expected = Set.of(Set.of(0, 1), Set.of(1, 2));
+        assertEquals(expected, result);
+    }
+
+    @Test
+    @DisplayName("Disconnected graph finds cliques per component")
+    void disconnectedGraph() {
+        List<Set<Integer>> adjacency = buildGraph(5);
+        addUndirectedEdge(adjacency, 0, 1);
+        addUndirectedEdge(adjacency, 0, 2);
+        addUndirectedEdge(adjacency, 1, 2);
+        addUndirectedEdge(adjacency, 3, 4);
+
+        List<Set<Integer>> cliques = BronKerbosch.findMaximalCliques(adjacency);
+        Set<Set<Integer>> result = new HashSet<>(cliques);
+        Set<Set<Integer>> expected = Set.of(Set.of(0, 1, 2), Set.of(3, 4));
+        assertEquals(expected, result);
+    }
+
+    @Test
+    @DisplayName("Null neighbor set triggers exception")
+    void nullNeighborSet() {
+        List<Set<Integer>> adjacency = new ArrayList<>();
+        adjacency.add(null);
+        assertThrows(IllegalArgumentException.class, () -> BronKerbosch.findMaximalCliques(adjacency));
+    }
+
+    private static List<Set<Integer>> buildGraph(int n) {
+        List<Set<Integer>> graph = new ArrayList<>(n);
+        for (int i = 0; i < n; i++) {
+            graph.add(new HashSet<>());
+        }
+        return graph;
+    }
+
+    private static void addUndirectedEdge(List<Set<Integer>> graph, int u, int v) {
+        graph.get(u).add(v);
+        graph.get(v).add(u);
+    }
+}

src/test/java/com/thealgorithms/graph/EdmondsKarpTest.java

@@ -0,0 +1,48 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+class EdmondsKarpTest {
+
+    @Test
+    @DisplayName("Classic CLRS network yields max flow 23")
+    void clrsExample() {
+        int[][] capacity = {{0, 16, 13, 0, 0, 0}, {0, 0, 10, 12, 0, 0}, {0, 4, 0, 0, 14, 0}, {0, 0, 9, 0, 0, 20}, {0, 0, 0, 7, 0, 4}, {0, 0, 0, 0, 0, 0}};
+        int maxFlow = EdmondsKarp.maxFlow(capacity, 0, 5);
+        assertEquals(23, maxFlow);
+    }
+
+    @Test
+    @DisplayName("Disconnected network has zero flow")
+    void disconnectedGraph() {
+        int[][] capacity = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
+        int maxFlow = EdmondsKarp.maxFlow(capacity, 0, 2);
+        assertEquals(0, maxFlow);
+    }
+
+    @Test
+    @DisplayName("Source equals sink returns zero")
+    void sourceEqualsSink() {
+        int[][] capacity = {{0, 5}, {0, 0}};
+        int maxFlow = EdmondsKarp.maxFlow(capacity, 0, 0);
+        assertEquals(0, maxFlow);
+    }
+
+    @Test
+    @DisplayName("Invalid matrix throws exception")
+    void invalidMatrix() {
+        int[][] capacity = {{0, 1}, {1}};
+        assertThrows(IllegalArgumentException.class, () -> EdmondsKarp.maxFlow(capacity, 0, 1));
+    }
+
+    @Test
+    @DisplayName("Negative capacity is rejected")
+    void negativeCapacity() {
+        int[][] capacity = {{0, -1}, {0, 0}};
+        assertThrows(IllegalArgumentException.class, () -> EdmondsKarp.maxFlow(capacity, 0, 1));
+    }
+}