kopia lustrzana https://github.com/villares/sketch-a-day
339 wiersze
11 KiB
Python
339 wiersze
11 KiB
Python
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#*- coding: utf-8 -*-
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"""
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A simple Python graph class, demonstrating the essential facts and functionalities of graphs
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based on https://www.python-course.eu/graphs_python.php and https://www.python.org/doc/essays/graphs/
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"""
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from random import choice
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class Graph(object):
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def __init__(self, graph_dict=None):
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"""
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Initialize a graph object with dictionary provided,
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if none provided, create an empty one.
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"""
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if graph_dict is None:
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graph_dict = {}
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self.__graph_dict = graph_dict
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def __len__(self):
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return len(self.__graph_dict)
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def vertices(self):
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"""Return the vertices of graph."""
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return list(self.__graph_dict.keys())
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def edges(self):
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"""Return the edges of graph """
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return self.__generate_edges()
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def add_vertex(self, vertex):
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"""
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If the vertex "vertex" is not in self.__graph_dict,
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add key "vertex" with an empty list as a value,
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otherwise, do nothing.
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"""
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if vertex not in self.__graph_dict:
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self.__graph_dict[vertex] = []
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def add_edge(self, edge):
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"""
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Assuming that edge is of type set, tuple or list;
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add edge between vertices. Can add multiple edges!
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"""
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edge = set(edge)
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vertex1 = edge.pop()
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if edge:
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# not a loop
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vertex2 = edge.pop()
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if vertex1 in self.__graph_dict:
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self.__graph_dict[vertex1].append(vertex2)
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else:
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self.__graph_dict[vertex1] = [vertex2]
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if vertex2 in self.__graph_dict:
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self.__graph_dict[vertex2].append(vertex1)
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else:
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self.__graph_dict[vertex2] = [vertex1]
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else:
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# a loop
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if vertex1 in self.__graph_dict:
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self.__graph_dict[vertex1].append(vertex1)
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else:
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self.__graph_dict[vertex1] = [vertex1]
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def remove_vertex(self, vert):
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del self.__graph_dict[vert]
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for k in self.__graph_dict.keys():
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if vert in self.__graph_dict[k]:
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self.__graph_dict[k].remove(vert)
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def remove_edge(self, edge):
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edge = set(edge)
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vertex1 = edge.pop()
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if edge:
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vertex2 = edge.pop()
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self.__graph_dict[vertex1].remove(vertex2)
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self.__graph_dict[vertex2].remove(vertex1)
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else:
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self.__graph_dict[vertex1].remove(vertex1)
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def __generate_edges(self):
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"""
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Generate the edges, represented as sets with one
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(a loop back to the vertex) or two vertices.
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"""
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edges = []
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for vertex in self.__graph_dict:
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for neighbour in self.__graph_dict[vertex]:
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if {neighbour, vertex} not in edges:
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edges.append({vertex, neighbour})
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return edges
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def __str__(self):
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res = "vertices: "
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for k in self.__graph_dict:
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res += str(k) + " "
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res += "\nedges: "
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for edge in self.__generate_edges():
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res += str(edge) + " "
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return res
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def find_isolated_vertices(self):
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"""
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Return a list of isolated vertices.
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"""
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graph = self.__graph_dict
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isolated = []
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for vertex in graph:
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print(isolated, vertex)
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if not graph[vertex]:
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isolated += [vertex]
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return isolated
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def find_path(self, start_vertex, end_vertex, path=[]):
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"""
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Find a path from start_vertex to end_vertex in graph.
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"""
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graph = self.__graph_dict
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path = path + [start_vertex]
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if start_vertex == end_vertex:
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return path
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if start_vertex not in graph:
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return None
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for vertex in graph[start_vertex]:
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if vertex not in path:
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extended_path = self.find_path(vertex,
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end_vertex,
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path)
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if extended_path:
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return extended_path
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return None
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def find_all_paths(self, start_vertex, end_vertex, path=[]):
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"""
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Find all paths from start_vertex to end_vertex.
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"""
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graph = self.__graph_dict
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path = path + [start_vertex]
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if start_vertex == end_vertex:
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return [path]
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if start_vertex not in graph:
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return []
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paths = []
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for vertex in graph[start_vertex]:
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if vertex not in path:
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extended_paths = self.find_all_paths(vertex,
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end_vertex,
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path)
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for p in extended_paths:
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paths.append(p)
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return paths
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def is_connected(self,
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vertices_encountered=None,
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start_vertex=None):
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"""Find if the graph is connected."""
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if vertices_encountered is None:
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vertices_encountered = set()
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gdict = self.__graph_dict
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vertices = list(gdict.keys()) # "list" necessary in Python 3
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if not start_vertex:
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# chosse a vertex from graph as a starting point
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start_vertex = vertices[0]
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vertices_encountered.add(start_vertex)
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if len(vertices_encountered) != len(vertices):
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for vertex in gdict[start_vertex]:
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if vertex not in vertices_encountered:
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if self.is_connected(vertices_encountered, vertex):
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return True
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else:
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return True
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return False
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def vertex_degree(self, vertex):
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"""
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Return the number of edges connecting to a vertex (the number of adjacent vertices).
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Loops are counted double, i.e. every occurence of vertex in the list of adjacent vertices.
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"""
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adj_vertices = self.__graph_dict[vertex]
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degree = len(adj_vertices) + adj_vertices.count(vertex)
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return degree
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def degree_sequence(self):
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"""Calculates the degree sequence."""
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seq = []
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for vertex in self.__graph_dict:
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seq.append(self.vertex_degree(vertex))
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seq.sort(reverse=True)
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return tuple(seq)
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@staticmethod
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def is_degree_sequence(sequence):
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"""
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Return True, if the sequence is a degree sequence (non-increasing),
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otherwise return False.
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"""
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return all(x >= y for x, y in zip(sequence, sequence[1:]))
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def delta(self):
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"""Find minimum degree of vertices."""
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min = 100000000
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for vertex in self.__graph_dict:
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vertex_degree = self.vertex_degree(vertex)
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if vertex_degree < min:
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min = vertex_degree
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return min
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def Delta(self):
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"""Finde maximum degree of vertices."""
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max = 0
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for vertex in self.__graph_dict:
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vertex_degree = self.vertex_degree(vertex)
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if vertex_degree > max:
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max = vertex_degree
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return max
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def density(self):
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"""Calculate the graph density."""
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g = self.__graph_dict
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V = len(g.keys())
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E = len(self.edges())
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return 2.0 * E / (V * (V - 1))
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def diameter(self):
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"""Calculates the graph diameter."""
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v = self.vertices()
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pairs = [
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(v[i],
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v[j]) for i in range(
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len(v)) for j in range(
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i + 1,
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len(v) - 1)]
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smallest_paths = []
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for (s, e) in pairs:
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paths = self.find_all_paths(s, e)
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smallest = sorted(paths, key=len)[0]
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smallest_paths.append(smallest)
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smallest_paths.sort(key=len)
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# longest path is at the end of list,
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# i.e. diameter corresponds to the length of this path
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diameter = len(smallest_paths[-1]) - 1
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return diameter
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@staticmethod
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def erdoes_gallai(dsequence):
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"""
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Check if Erdoes-Gallai inequality condition is fullfilled.
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"""
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if sum(dsequence) % 2:
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# sum of sequence is odd
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return False
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if Graph.is_degree_sequence(dsequence):
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for k in range(1, len(dsequence) + 1):
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left = sum(dsequence[:k])
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right = k * (k - 1) + sum([min(x, k) for x in dsequence[k:]])
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if left > right:
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return False
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else:
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# sequence is increasing
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return False
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return True
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# Code by Eryk Kopczyński
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def find_shortest_path(self, start, end):
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from collections import deque
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graph = self.__graph_dict
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dist = {start: [start]}
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q = deque((start,))
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while len(q):
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at = q.popleft()
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for next in graph[at]:
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if next not in dist:
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# dist[next] = [dist[at], next]
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# less efficient but nicer output
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dist[next] = dist[at] + [next]
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q.append(next)
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return dist.get(end)
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##############
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def is_cyclic(self):
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"""
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Returns true if the graph contains a cycle, else false.
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"""
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# Mark all the vertices as not visited
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visited = [False] * len(self)
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# Call helper function to detect cycle in different DFS trees
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for i, v in enumerate(visited):
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# Don't recur for u if it is already visited
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if v == False:
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if self.dfs(i, visited, -1):
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return True
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return False
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def dfs(self, v, visited, parent):
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# Mark the current node as visited
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visited[v] = True
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# Recur for all the vertices adjacent to this vertex
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for i in self.__graph_dict[v]:
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# If the node is not visited then recurse on it
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if visited[i] == False:
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if(self.dfs(i, visited, v)):
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return True
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# If an adjacent vertex is visited and not parent of current
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# vertex, then there is a cycle
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elif parent != i:
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return True
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return False
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##############
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def get_random_vertex(self):
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return choice(self.vertices())
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@staticmethod
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def random_graph(names,
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connect_rate=.9,
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allow_loops=True,
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allow_cyclic=False,
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connected=False):
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vertices = set(names)
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while True:
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graph = Graph()
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for v in vertices:
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graph.add_vertex(v)
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if random(1) < connect_rate:
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if allow_loops:
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names = list(vertices)
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else:
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names = list(vertices - set((v,)))
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graph.add_edge({v, choice(names)})
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if not connected or graph.is_connected():
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if allow_cyclic or not graph.is_cyclic():
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break
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return graph
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