Added graphs python code

Added python script which demnostrates a graph data structure,
with some basic methods (operators).

graphing/graph.py

@@ -0,0 +1,122 @@
+"""
+:Author: James Sherratt
+:Date: 20/10/2019
+:License: MIT
+
+:name: graph.py
+"""
+
+
+class Graph:
+
+    def __init__(self):
+        self.vertices = set()
+        self.edges = set()
+
+    def add_vertex(self, vert):
+        """
+        Add a vertex to the graph.
+
+        :param vert: name of the vertex.
+        :return: None
+        """
+        self.vertices.add(vert)
+
+    def add_edge(self, vert1, vert2, directional=False):
+        """
+        Add an edge to the graph. The edge will be defined as a simple tuple where:
+        - The first value is the initial edge.
+        - The second is the final edge.
+        - The third is whether the edge is directional.
+
+        :param vert1: the start vertex.
+        :param vert2: the end vertex.
+        :param directional: whether or not the edge has a direction. Default: False
+        :return: None
+        """
+        self.vertices.add(vert1)
+        self.vertices.add(vert2)
+        if (not directional) and (vert1 > vert2):
+            # swap if not directional to avoid duplicates in the set.
+            self.edges.add((vert2, vert1, directional))
+        else:
+            self.edges.add((vert1, vert2, directional))
+
+    def adjacency(self, vert1, vert2):
+        """
+        Check if 2 vertices are adjacent (if they exist). Note: if vert1 and vert2
+        are connected, but directionally from vert2 to vert1, False is returned.
+
+        :param vert1: The first vertex to compare.
+        :param vert2: The second vertex to compare.
+        :return: True if adjacent, False if not, None if either are not in the set.
+        """
+        if (vert1 not in self.vertices) or (vert2 not in self.vertices):
+            return None
+
+        for edge in self.edges:
+            if (vert1 == edge[0]) and (vert2 == edge[1]):
+                return True
+            if (not edge[2]) and ((vert1 == edge[1]) and (vert2 == edge[0])):
+                return True
+        return False
+
+    def neighbours(self, vert):
+        """
+        Get the neighbours of a vertex.
+        :param vert: name of the vertex.
+        :return: list of neighbours, or None if the vertex is not in the graph.
+        """
+        if vert not in self.vertices:
+            return None
+
+        neighbours = set()
+        for edge in self.edges:
+            if vert == edge[0]:
+                neighbours.add(edge[1])
+            elif (not edge[2]) and (vert == edge[1]):
+                neighbours.add(edge[0])
+        return neighbours
+
+    def as_dict(self):
+        """
+        Convert the graph to a dictionary where:
+        - Each key is a vertex.
+        - Each value is a set of neighbours you can travel to.
+
+        :return: dict representing the graph.
+        """
+        graph_dict = {v: set() for v in self.vertices}
+        for edge in self.edges:
+            graph_dict[edge[0]].add(edge[1])
+            if not edge[2]:
+                graph_dict[edge[1]].add(edge[0])
+
+        return graph_dict
+
+
+if __name__ == "__main__":
+    mygraph = Graph()
+    mygraph.add_edge("a", "b")
+    mygraph.add_edge("b", "c")
+    mygraph.add_edge("b", "d")
+    mygraph.add_edge("c", "b")
+    mygraph.add_edge("a", "e", directional=True)
+    mygraph.add_vertex("z")
+    print("b neighbours:", mygraph.neighbours("b"))
+    print("a neighbours:", mygraph.neighbours("a"))
+    print("q neighbours:", mygraph.neighbours("q"))
+    print("e neighbours:", mygraph.neighbours("e"))
+    print()
+    # Adjacency has direction.
+    print("a and e adjacent:", mygraph.adjacency("a", "e"))
+    print("e and a adjacent:", mygraph.adjacency("e", "a"))
+    print("d and b adjacent", mygraph.adjacency("d", "b"))
+    print("q and a adjacent:", mygraph.adjacency("q", "a"))
+    print("z and a adjacent:", mygraph.adjacency("z", "a"))
+    print()
+    print("as dict")
+    print(mygraph.as_dict())
+
+    # Exercise/ project: add a method "path" to find path between 2 vertices.
+    # (Hint: lookup DFS/ BFS algorithm.)