public void FindFurthestVertex3()
{
// This graph is a line broken in two.
var graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 3, 4 }, { 4, 5 }
});
Assert.AreEqual(2, graph.FindFurthestVertex(0).Item1.ID);
Assert.AreEqual(2, graph.FindFurthestVertex(0).Item2);
Assert.IsTrue(graph.FindFurthestVertex(1).Item1.ID == 2 ||
graph.FindFurthestVertex(1).Item1.ID == 0);
Assert.AreEqual(1, graph.FindFurthestVertex(1).Item2);
Assert.AreEqual(0, graph.FindFurthestVertex(2).Item1.ID);
Assert.AreEqual(2, graph.FindFurthestVertex(2).Item2);
Assert.AreEqual(5, graph.FindFurthestVertex(3).Item1.ID);
Assert.AreEqual(2, graph.FindFurthestVertex(3).Item2);
Assert.IsTrue(graph.FindFurthestVertex(4).Item1.ID == 3 ||
graph.FindFurthestVertex(4).Item1.ID == 5);
Assert.AreEqual(1, graph.FindFurthestVertex(4).Item2);
Assert.AreEqual(3, graph.FindFurthestVertex(5).Item1.ID);
Assert.AreEqual(2, graph.FindFurthestVertex(5).Item2);
}
public void ValidatesAGraph1()
{
// This graph is a triangle.
var graph = SimpleGraph.CreateFromZeroBasedEdges(3, new[, ]
{
{ 0, 1 }, { 0, 2 }, { 1, 2 }
});
Assert.AreEqual(2, graph.Vertices[0].Degree);
Assert.AreEqual(2, graph.Vertices[1].Degree);
Assert.AreEqual(2, graph.Vertices[2].Degree);
Assert.IsTrue(graph.HasEdge(0, 1));
Assert.IsTrue(graph.HasEdge(1, 0));
Assert.IsTrue(graph.HasEdge(0, 2));
Assert.IsTrue(graph.HasEdge(1, 2));
Assert.IsFalse(graph.HasEdge(1, 1));
Assert.IsFalse(graph.Vertices[0].HasNeighbor(0));
Assert.IsTrue(graph.Vertices[0].HasNeighbor(1));
Assert.IsTrue(graph.Vertices[0].HasNeighbor(2));
Assert.IsTrue(graph.Vertices[1].HasNeighbor(0));
Assert.IsFalse(graph.Vertices[1].HasNeighbor(1));
Assert.IsTrue(graph.Vertices[1].HasNeighbor(2));
Assert.IsTrue(graph.Vertices[2].HasNeighbor(0));
Assert.IsTrue(graph.Vertices[2].HasNeighbor(1));
Assert.IsFalse(graph.Vertices[2].HasNeighbor(2));
}
public void FindFurthestVertex2()
{
// This graph is a line.
var graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }
});
Assert.AreEqual(5, graph.FindFurthestVertex(0).Item1.ID);
Assert.AreEqual(5, graph.FindFurthestVertex(0).Item2);
Assert.AreEqual(5, graph.FindFurthestVertex(1).Item1.ID);
Assert.AreEqual(4, graph.FindFurthestVertex(1).Item2);
Assert.AreEqual(5, graph.FindFurthestVertex(2).Item1.ID);
Assert.AreEqual(3, graph.FindFurthestVertex(2).Item2);
Assert.AreEqual(0, graph.FindFurthestVertex(3).Item1.ID);
Assert.AreEqual(3, graph.FindFurthestVertex(3).Item2);
Assert.AreEqual(0, graph.FindFurthestVertex(4).Item1.ID);
Assert.AreEqual(4, graph.FindFurthestVertex(4).Item2);
Assert.AreEqual(0, graph.FindFurthestVertex(5).Item1.ID);
Assert.AreEqual(5, graph.FindFurthestVertex(5).Item2);
}
public void FindFurthestVertex1()
{
// This graph is a point.
var graph = SimpleGraph.CreateFromZeroBasedEdges(1, new int[, ] {
});
Assert.AreEqual(0, graph.FindFurthestVertex(0).Item1.ID);
Assert.AreEqual(0, graph.FindFurthestVertex(0).Item2);
}
public void ValidatesAGraph2()
{
// This graph is two lines and a point.
var graph = SimpleGraph.CreateFromZeroBasedEdges(5, new[, ]
{
{ 0, 1 }, { 2, 3 }
});
Assert.AreEqual(1, graph.Vertices[0].Degree);
Assert.AreEqual(1, graph.Vertices[1].Degree);
Assert.AreEqual(1, graph.Vertices[2].Degree);
Assert.AreEqual(1, graph.Vertices[3].Degree);
Assert.AreEqual(0, graph.Vertices[4].Degree);
Assert.IsTrue(graph.HasEdge(0, 1));
Assert.IsTrue(graph.HasEdge(2, 3));
Assert.IsFalse(graph.HasEdge(2, 0));
Assert.IsFalse(graph.HasEdge(0, 3));
Assert.IsFalse(graph.HasEdge(1, 2));
Assert.IsFalse(graph.HasEdge(3, 1));
for (int i = 0; i <= 4; ++i)
{
Assert.IsFalse(graph.HasEdge(4, i));
}
Assert.IsFalse(graph.Vertices[0].HasNeighbor(0));
Assert.IsTrue(graph.Vertices[0].HasNeighbor(1));
Assert.IsFalse(graph.Vertices[0].HasNeighbor(2));
Assert.IsFalse(graph.Vertices[0].HasNeighbor(3));
Assert.IsFalse(graph.Vertices[0].HasNeighbor(4));
Assert.IsTrue(graph.Vertices[1].HasNeighbor(0));
Assert.IsFalse(graph.Vertices[1].HasNeighbor(1));
Assert.IsFalse(graph.Vertices[1].HasNeighbor(2));
Assert.IsFalse(graph.Vertices[1].HasNeighbor(3));
Assert.IsFalse(graph.Vertices[1].HasNeighbor(4));
Assert.IsFalse(graph.Vertices[2].HasNeighbor(0));
Assert.IsFalse(graph.Vertices[2].HasNeighbor(1));
Assert.IsFalse(graph.Vertices[2].HasNeighbor(2));
Assert.IsTrue(graph.Vertices[2].HasNeighbor(3));
Assert.IsFalse(graph.Vertices[2].HasNeighbor(4));
Assert.IsFalse(graph.Vertices[3].HasNeighbor(0));
Assert.IsFalse(graph.Vertices[3].HasNeighbor(1));
Assert.IsTrue(graph.Vertices[3].HasNeighbor(2));
Assert.IsFalse(graph.Vertices[3].HasNeighbor(3));
Assert.IsFalse(graph.Vertices[3].HasNeighbor(4));
Assert.IsFalse(graph.Vertices[4].HasNeighbor(0));
Assert.IsFalse(graph.Vertices[4].HasNeighbor(1));
Assert.IsFalse(graph.Vertices[4].HasNeighbor(2));
Assert.IsFalse(graph.Vertices[4].HasNeighbor(3));
Assert.IsFalse(graph.Vertices[4].HasNeighbor(4));
}
public void IsConnected2()
{
// This graph is two lines and a point.
var graph = SimpleGraph.CreateFromZeroBasedEdges(5, new[, ]
{
{ 0, 1 }, { 2, 3 }
});
Assert.IsFalse(graph.IsConnected());
}
public void IsConnected1()
{
// This graph is a triangle.
var graph = SimpleGraph.CreateFromZeroBasedEdges(3, new[, ]
{
{ 0, 1 }, { 0, 2 }, { 1, 2 }
});
Assert.IsTrue(graph.IsConnected());
}
public void FindFurthestVertex4()
{
// This graph is complete with four vertices.
var graph = SimpleGraph.CreateFromZeroBasedEdges(4, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 0 }, { 0, 2 }, { 3, 1 }
});
Assert.AreEqual(1, graph.FindFurthestVertex(0).Item2);
Assert.AreEqual(1, graph.FindFurthestVertex(1).Item2);
Assert.AreEqual(1, graph.FindFurthestVertex(2).Item2);
Assert.AreEqual(1, graph.FindFurthestVertex(3).Item2);
}
public void IsConnected4()
{
// This graph is a line.
var graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }
});
Assert.IsTrue(graph.IsConnected());
var graphBrokenInTwo = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 3, 4 }, { 4, 5 }
});
Assert.IsFalse(graphBrokenInTwo.IsConnected());
}
public void IsConnected3()
{
// This graph is B-shaped.
var graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 5, 0 }, { 2, 5 }
});
Assert.IsTrue(graph.IsConnected());
var graphWithOneExtra = SimpleGraph.CreateFromZeroBasedEdges(7, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 5, 0 }, { 2, 5 }
});
Assert.IsFalse(graphWithOneExtra.IsConnected());
}
public void FindFurthestVertex5()
{
// This graph is a weird mess: http://i.imgur.com/kbeOrqA.png.
var graph = SimpleGraph.CreateFromZeroBasedEdges(9, new[, ]
{
{ 0, 1 }, { 0, 3 }, { 0, 4 }, { 0, 5 }, { 1, 2 }, { 1, 3 }, { 1, 6 },
{ 2, 3 }, { 2, 4 }, { 3, 4 }, { 4, 5 }, { 4, 8 }, { 5, 7 }
});
Assert.AreEqual(2, graph.FindFurthestVertex(0).Item2);
Assert.AreEqual(3, graph.FindFurthestVertex(1).Item2);
Assert.AreEqual(3, graph.FindFurthestVertex(2).Item2);
Assert.AreEqual(3, graph.FindFurthestVertex(3).Item2);
Assert.AreEqual(3, graph.FindFurthestVertex(4).Item2);
Assert.AreEqual(3, graph.FindFurthestVertex(5).Item2);
Assert.AreEqual(4, graph.FindFurthestVertex(6).Item2);
Assert.AreEqual(4, graph.FindFurthestVertex(7).Item2);
Assert.AreEqual(4, graph.FindFurthestVertex(8).Item2);
}
public void GetShortestPathLength_ForSmallGraphs()
{
// This graph has a single vertex.
var graph = SimpleGraph.CreateFromZeroBasedEdges(1, new int[, ] {
});
Assert.AreEqual(0, graph.GetShortestPathLength(0, 0));
// This graph has two vertices.
graph = SimpleGraph.CreateFromZeroBasedEdges(2, new int[, ] {
});
Assert.AreEqual(0, graph.GetShortestPathLength(0, 0));
Assert.AreEqual(0, graph.GetShortestPathLength(1, 1));
Assert.AreEqual(-1, graph.GetShortestPathLength(1, 0));
// This graph has two vertices connected by an edge.
graph = SimpleGraph.CreateFromZeroBasedEdges(2, new[, ]
{
{ 0, 1 }
});
Assert.AreEqual(0, graph.GetShortestPathLength(1, 1));
Assert.AreEqual(1, graph.GetShortestPathLength(0, 1));
// This graph has 6 vertices, with pairs connected.
graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 2, 3 }, { 4, 5 }
});
Assert.AreEqual(1, graph.GetShortestPathLength(0, 1));
Assert.AreEqual(1, graph.GetShortestPathLength(2, 3));
Assert.AreEqual(1, graph.GetShortestPathLength(4, 5));
Assert.AreEqual(-1, graph.GetShortestPathLength(3, 5));
// This graph has 6 vertices, connected in a line.
graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }
});
for (int i = 0; i <= 5; ++i)
{
for (int j = 0; j <= 5; ++j)
{
Assert.AreEqual(Math.Abs(i - j), graph.GetShortestPathLength(i, j));
}
}
// This graph has 6 vertices, connected in a circle.
graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 5, 0 }
});
Assert.AreEqual(1, graph.GetShortestPathLength(3, 2));
Assert.AreEqual(1, graph.GetShortestPathLength(5, 0));
Assert.AreEqual(2, graph.GetShortestPathLength(5, 1));
Assert.AreEqual(2, graph.GetShortestPathLength(2, 4));
// This graph has 9 vertices, 6 connected in a line, 3 in a triangle.
graph = SimpleGraph.CreateFromZeroBasedEdges(9, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 6, 7 }, { 7, 8 }, { 8, 6 }
});
for (int i = 0; i <= 5; ++i)
{
for (int j = 0; j <= 5; ++j)
{
Assert.AreEqual(Math.Abs(i - j), graph.GetShortestPathLength(i, j));
}
}
Assert.AreEqual(-1, graph.GetShortestPathLength(2, 6));
Assert.AreEqual(1, graph.GetShortestPathLength(6, 7));
Assert.AreEqual(1, graph.GetShortestPathLength(6, 8));
Assert.AreEqual(1, graph.GetShortestPathLength(7, 8));
// This graph has 12 vertices, 6 connected in a line, 4 in a square, 2 in a line.
graph = SimpleGraph.CreateFromZeroBasedEdges(12, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 6, 7 }, { 7, 8 }, { 8, 9 }, { 9, 6 }, { 10, 11 }
});
Assert.AreEqual(1, graph.GetShortestPathLength(10, 11));
Assert.AreEqual(2, graph.GetShortestPathLength(6, 8));
Assert.AreEqual(-1, graph.GetShortestPathLength(6, 3));
Assert.AreEqual(3, graph.GetShortestPathLength(4, 1));
}
public void IsBipartite_ForSmallGraphs()
{
// This graph is empty.
var graph = SimpleGraph.CreateFromZeroBasedEdges(0, new int[, ] {
});
Assert.IsTrue(graph.IsBipartite());
// This graph has a single vertex.
graph = SimpleGraph.CreateFromZeroBasedEdges(1, new int[, ] {
});
Assert.IsTrue(graph.IsBipartite());
// This graph has two vertices.
graph = SimpleGraph.CreateFromZeroBasedEdges(2, new int[, ] {
});
Assert.IsTrue(graph.IsBipartite());
// This graph has two vertices connected by an edge.
graph = SimpleGraph.CreateFromZeroBasedEdges(2, new[, ]
{
{ 0, 1 }
});
Assert.IsTrue(graph.IsBipartite());
// This graph has 6 vertices, with pairs connected.
graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 2, 3 }, { 4, 5 }
});
Assert.IsTrue(graph.IsBipartite());
// This graph has 6 vertices, connected in a line.
graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }
});
Assert.IsTrue(graph.IsBipartite());
// This graph has 6 vertices, connected in a circle.
graph = SimpleGraph.CreateFromZeroBasedEdges(6, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 5, 0 }
});
Assert.IsTrue(graph.IsBipartite());
// This graph has 7 vertices, connected in a circle.
graph = SimpleGraph.CreateFromZeroBasedEdges(7, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 5, 6 }, { 6, 0 }
});
Assert.IsFalse(graph.IsBipartite());
// This graph has 9 vertices, 6 connected in a line, 3 in a triangle.
graph = SimpleGraph.CreateFromZeroBasedEdges(9, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 6, 7 }, { 7, 8 }, { 8, 6 }
});
Assert.IsFalse(graph.IsBipartite());
// This graph has 12 vertices, 6 connected in a line, 4 in a square, 2 in a line.
graph = SimpleGraph.CreateFromZeroBasedEdges(12, new[, ]
{
{ 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 }, { 6, 7 }, { 7, 8 }, { 8, 9 }, { 9, 6 }, { 10, 11 }
});
Assert.IsTrue(graph.IsBipartite());
// This graph has 7 vertices, 2 connected in a line, 2 in a line, 3 in a triangle
graph = SimpleGraph.CreateFromZeroBasedEdges(12, new[, ]
{
{ 0, 1 }, { 2, 3 }, { 4, 5 }, { 5, 6 }, { 6, 4 }
});
Assert.IsFalse(graph.IsBipartite());
}