14a graphs!

2020/sketch_2020_07_14a/graph.py

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+#*- coding: utf-8 -*-
+
+"""
+A simple Python graph class, demonstrating the essential facts and functionalities of graphs
+based on https://www.python-course.eu/graphs_python.php and https://www.python.org/doc/essays/graphs/
+"""
+
+class Graph(object):
+
+    def __init__(self, graph_dict=None):
+        """
+        Initialize a graph object with dictionary provided,
+        if none provided, create an empty one.
+        """
+        if graph_dict is None:
+            graph_dict = {}
+        self.__graph_dict = graph_dict
+
+    def __len__(self):
+        return len(self.__graph_dict)
+    
+    def __iter__(self):
+        return iter(self.__graph_dict.keys())
+    
+    def __getitem__(self, i):
+        return self.__graph_dict[i]
+
+    def vertices(self):
+        """Return the vertices of graph."""
+        return list(self.__graph_dict.keys())
+
+    def edges(self):
+        """Return the edges of graph """
+        return self.__generate_edges()
+
+    def add_vertex(self, vertex):
+        """
+        If the vertex "vertex" is not in self.__graph_dict,
+        add key "vertex" with an empty list as a value,
+        otherwise, do nothing.
+        """
+        if vertex not in self.__graph_dict:
+            self.__graph_dict[vertex] = []
+
+    def add_edge(self, edge):
+        """
+        Assuming that edge is of type set, tuple or list;
+        add edge between vertices. Can add multiple edges!
+        """
+        edge = set(edge)
+        vertex1 = edge.pop()
+        if edge:
+            # not a loop
+            vertex2 = edge.pop()
+        else:
+            # a loop
+            vertex2 = vertex1
+        if vertex1 in self.__graph_dict:
+            self.__graph_dict[vertex1].append(vertex2)
+        else:
+            self.__graph_dict[vertex1] = [vertex2]
+
+    def __generate_edges(self):
+        """
+        Generate the edges, represented as sets with one
+        (a loop back to the vertex) or two vertices.
+        """
+        edges = []
+        for vertex in self.__graph_dict:
+            for neighbour in self.__graph_dict[vertex]:
+                if {neighbour, vertex} not in edges:
+                    edges.append({vertex, neighbour})
+        return edges
+
+    def __str__(self):
+        res = "vertices: "
+        for k in self.__graph_dict:
+            res += str(k) + " "
+        res += "\nedges: "
+        for edge in self.__generate_edges():
+            res += str(edge) + " "
+        return res
+
+    def find_isolated_vertices(self):
+        """
+        Return a list of isolated vertices.
+        """
+        graph = self.__graph_dict
+        isolated = []
+        for vertex in graph:
+            print(isolated, vertex)
+            if not graph[vertex]:
+                isolated += [vertex]
+        return isolated
+
+    def find_path(self, start_vertex, end_vertex, path=[]):
+        """
+        Find a path from start_vertex to end_vertex in graph.
+        """
+        graph = self.__graph_dict
+        path = path + [start_vertex]
+        if start_vertex == end_vertex:
+            return path
+        if start_vertex not in graph:
+            return None
+        for vertex in graph[start_vertex]:
+            if vertex not in path:
+                extended_path = self.find_path(vertex,
+                                               end_vertex,
+                                               path)
+                if extended_path:
+                    return extended_path
+        return None
+
+    def find_all_paths(self, start_vertex, end_vertex, path=[]):
+        """
+        Find all paths from start_vertex to end_vertex.
+        """
+        graph = self.__graph_dict
+        path = path + [start_vertex]
+        if start_vertex == end_vertex:
+            return [path]
+        if start_vertex not in graph:
+            return []
+        paths = []
+        for vertex in graph[start_vertex]:
+            if vertex not in path:
+                extended_paths = self.find_all_paths(vertex,
+                                                     end_vertex,
+                                                     path)
+                for p in extended_paths:
+                    paths.append(p)
+        return paths
+
+    def is_connected(self,
+                     vertices_encountered=None,
+                     start_vertex=None):
+        """Find if the graph is connected."""
+        if vertices_encountered is None:
+            vertices_encountered = set()
+        gdict = self.__graph_dict
+        vertices = list(gdict.keys())  # "list" necessary in Python 3
+        if not start_vertex:
+            # chosse a vertex from graph as a starting point
+            start_vertex = vertices[0]
+        vertices_encountered.add(start_vertex)
+        if len(vertices_encountered) != len(vertices):
+            for vertex in gdict[start_vertex]:
+                if vertex not in vertices_encountered:
+                    if self.is_connected(vertices_encountered, vertex):
+                        return True
+        else:
+            return True
+        return False
+
+    def vertex_degree(self, vertex):
+        """
+        Return the number of edges connecting to a vertex (the number of adjacent vertices).
+        Loops are counted double, i.e. every occurence of vertex in the list of adjacent vertices.
+        """
+        adj_vertices = self.__graph_dict[vertex]
+        degree = len(adj_vertices) + adj_vertices.count(vertex)
+        return degree
+
+    def degree_sequence(self):
+        """Calculates the degree sequence."""
+        seq = []
+        for vertex in self.__graph_dict:
+            seq.append(self.vertex_degree(vertex))
+        seq.sort(reverse=True)
+        return tuple(seq)
+
+    @staticmethod
+    def is_degree_sequence(sequence):
+        """
+        Return True, if the sequence is a degree sequence (non-increasing),
+        otherwise return False.
+        """
+        return all(x >= y for x, y in zip(sequence, sequence[1:]))
+
+    def delta(self):
+        """Find minimum degree of vertices."""
+        min = 100000000
+        for vertex in self.__graph_dict:
+            vertex_degree = self.vertex_degree(vertex)
+            if vertex_degree < min:
+                min = vertex_degree
+        return min
+
+    def Delta(self):
+        """Finde maximum degree of vertices."""
+        max = 0
+        for vertex in self.__graph_dict:
+            vertex_degree = self.vertex_degree(vertex)
+            if vertex_degree > max:
+                max = vertex_degree
+        return max
+
+    def density(self):
+        """Calculate the graph density."""
+        g = self.__graph_dict
+        V = len(g.keys())
+        E = len(self.edges())
+        return 2.0 * E / (V * (V - 1))
+
+    def diameter(self):
+        """Calculates the graph diameter."""
+
+        v = self.vertices()
+        pairs = [
+            (v[i],
+             v[j]) for i in range(
+                len(v)) for j in range(
+                i + 1,
+                len(v) - 1)]
+        smallest_paths = []
+        for (s, e) in pairs:
+            paths = self.find_all_paths(s, e)
+            smallest = sorted(paths, key=len)[0]
+            smallest_paths.append(smallest)
+
+        smallest_paths.sort(key=len)
+
+        # longest path is at the end of list,
+        # i.e. diameter corresponds to the length of this path
+        diameter = len(smallest_paths[-1]) - 1
+        return diameter
+
+    @staticmethod
+    def erdoes_gallai(dsequence):
+        """
+        Check if Erdoes-Gallai inequality condition is fullfilled.
+        """
+        if sum(dsequence) % 2:
+            # sum of sequence is odd
+            return False
+        if Graph.is_degree_sequence(dsequence):
+            for k in range(1, len(dsequence) + 1):
+                left = sum(dsequence[:k])
+                right = k * (k - 1) + sum([min(x, k) for x in dsequence[k:]])
+                if left > right:
+                    return False
+        else:
+            # sequence is increasing
+            return False
+        return True
+
+
+    # Code by Eryk Kopczyński
+    def find_shortest_path(self, start, end):
+        from collections import deque
+        graph = self.__graph_dict
+        dist = {start: [start]}
+        q = deque(start)
+        while len(q):
+            at = q.popleft()
+            for next in graph[at]:
+                if next not in dist:
+                    #dist[next] = [dist[at], next] 
+                    dist[next] = dist[at]+[next]   # less efficient but nicer output
+                    q.append(next)
+        return dist.get(end)

2020/sketch_2020_07_14a/sketch_2020_07_14a.pyde

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+from graph import Graph
+
+graph = Graph({"g": ["d", "f"],
+               "i": ["c"],
+               "c": ["i", "c", "d", "e"],
+               "d": ["f", "c"],
+               "e": ["c"],
+               "f": ["d", "h"],
+               "a": ["b"],
+               "h": ["f"],
+               "b": ["a"]
+               })
+
+
+def setup():
+    size(500, 500)
+    noLoop()
+    setup_graph(graph)
+    fill(0)
+    textSize(18)
+    textAlign(CENTER, CENTER)
+    stroke(255)
+    strokeWeight(3)
+
+def draw():
+    for v in grid.keys():
+        xa, ya = grid[v]
+        for e in graph[v]:
+            xb, yb = grid[e]
+            line(xa, ya, xb, yb)
+    
+    for v in grid.keys():
+        x, y = grid[v]
+        text(v, x, y)
+
+    saveFrame("sketch_2020_07_14a.png")
+
+def setup_graph(g):
+    global cols, rows, grid
+    cols, rows = dimensionar_grade(len(g))
+    w, h = width / cols, height / rows
+    grid = {}
+    v_list = g.vertices() 
+    for c in range(cols):
+        for r in range(rows):
+            if v_list:
+                v = v_list.pop()
+                grid[v] = (w /2 + c * w,
+                           h /2 + r * h)
+                
+
+def dimensionar_grade(n):
+    a = int(sqrt(n))
+    b = n / a
+    if a * b < n:
+        b += 1
+    print(u'{}: {} × {} ({})'.format(n, a, b, a * b))
+    return a, b
+
+def keyPressed():
+    global n
+    redraw()
+    if str(key) in '+=':
+        n += 1
+    if key == '-' and n > 2:
+        n -= 1