Add triangle counting implementation and simple test

data/tc_test.csv

@@ -0,0 +1,16 @@
+FROM,TO,DIST
+A,B,1
+A,C,1
+A,D,1
+A,E,1
+B,C,1
+B,D,1
+B,E,1
+C,D,1
+E,C,1
+D,E,1
+B,F,1
+E,F,1
+E,G,1
+F,H,1
+G,H,1

include/graph/algorithm/tc.hpp

@@ -0,0 +1,73 @@
+/**
+ * @file tc.hpp
+ * 
+ * @brief Minimum spanning tree using Kruskal's and Prim's algorithms.
+ * 
+ * @copyright Copyright (c) 2022
+ * 
+ * SPDX-License-Identifier: BSL-1.0
+ *
+ * @authors
+ *   Andrew Lumsdaine
+ *   Phil Ratzloff
+ *   Kevin Deweese
+ */
+
+#include "graph/graph.hpp"
+
+#ifndef GRAPH_MST_HPP
+#  define GRAPH_MST_HPP
+
+namespace std::graph {
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Find the number of triangles in a graph.
+ * 
+ * Complexity: O(|V|^3)
+ * 
+ * @tparam G          The graph type.
+ *
+ * @param g           The graph.
+ */
+template <adjacency_list G>
+requires ranges::random_access_range<vertex_range_t<G>> && integral<vertex_id_t<G>>
+size_t triangle_count(G&& g) {
+  size_t N(size(vertices(g)));
+  size_t triangles(0);
+
+  for (vertex_id_t<G> uid = 0; uid < N; ++uid) {
+    std::graph::incidence_iterator<G> i(g, uid);
+    auto ie = ranges::end(edges(g, uid));
+    while (i != ie) {
+      auto&& [vid, uv] = *i;
+      if(vid < uid) {
+        ++i;
+        continue;
+      }
+      std::graph::incidence_iterator<G> j(g, vid);
+      auto je = ranges::end(edges(g, vid));
+      auto i2 = i;
+
+      // Alternatively use std::set_intersection(i2, ie, j, je, counter) but this is slower
+      while (i2 != ie && j != je) {
+        auto&& [wid1, uw] = *i2;
+        auto&& [wid2, vw] = *j;
+        if (wid1 < wid2) {
+          ++i2;
+        } else if (wid2 < wid1) {
+          ++j;
+        } else {
+          ++triangles;
+          ++i2;
+          ++j;
+        }
+      }
+      ++i;
+    }
+  }
+  return triangles;
+}
+} // namespace std::graph
+
+#endif //GRAPH_MST_HPP

tests/CMakeLists.txt

@@ -47,6 +47,7 @@ set(UNITTEST_SOURCES
     "mis_tests.cpp" 
     "pagerank_tests.cpp"
     "mst_tests.cpp"
+    "tc_tests.cpp"
 )
 
 foreach(SOURCE IN LISTS UNITTEST_SOURCES)

tests/tc_tests.cpp

@@ -0,0 +1,25 @@
+#include <catch2/catch.hpp>
+#include "csv_routes.hpp"
+#include "graph/graph.hpp"
+#include "graph/algorithm/tc.hpp"
+#include "graph/container/dynamic_graph.hpp"
+#include "graph/views/incidence.hpp"
+#ifdef _MSC_VER
+#  include "Windows.h"
+#endif
+
+using std::cout;
+using std::endl;
+
+using routes_vol_graph_traits = std::graph::container::vol_graph_traits<double, std::string, std::string>;
+using routes_vol_graph_type   = std::graph::container::dynamic_adjacency_graph<routes_vol_graph_traits>;
+
+TEST_CASE("triangle counting test", "[tc]") {
+  init_console();
+
+  using G  = routes_vol_graph_type;
+  auto&& g = load_ordered_graph<G>(TEST_DATA_ROOT_DIR "tc_test.csv", name_order_policy::alphabetical, true);
+
+  size_t triangles = std::graph::triangle_count(g);
+  REQUIRE(triangles == 11);
+}