def random_connected_graph(n, m): """ Return the random connected graph G_{n,m}. Gives a graph picked randomly out of the set of all graphs with n nodes and m edges. Parameters ---------- n : int The number of nodes. m : int The number of edges. """ G = Graph() V = G + n # add n vertices max_edges = int((n * (n - 1.0)) / 2.0) m = min(m, max_edges) # add the first connection line, (n-1) edges, assuring a connected graph for u, v in pairwise(V): G.add_edge(u, v) AddEdge = G.add_edge E_star = set_copy(combinations(G.vertices, 2)) for u, v in random.sample(E_star - G.edges, m - n + 1): AddEdge(u, v) return G
def load_from_edge_list(strFileName, G = None): if G is None: G = Graph() with open(strFileName, 'r') as f: lines = f.readlines() if not G: G = Graph() v_list = dict() for line in lines: if len(line) == 0 or line == '\n': continue if line == "": continue fields = line.split() if not len(fields): continue if fields[0] == 'e': u = int(fields[1]) v = int(fields[2]) if u not in v_list: v_list[u] = G.add_vertex() if v not in v_list: v_list[v] = G.add_vertex() x, y = v_list[u], v_list[v] G.add_edge(x, y) return G
def complete_graph(N): G = Graph() G + N # add N vertices for u, v in combinations(G.Vertices(), 2): G.add_edge(u, v) return G
def from_nx_graph(G): """ Convert a graph from networkx graph to a custom class """ from planegraphs import Graph H = Graph() for v in G: H.add_named_vertex(v) for u, v in G.edges_iter(): H.add_edge(u, v) return H
def octahedron(): G = Graph() v, w, x, y, z1, z2 = (G.add_vertex() for i in xrange(6)) for i, j in pairwise((v, w, x, y, v)): G.add_edge(i, j) G.add_edge(i, z1) G.add_edge(i, z2) G.is_planar() return G
def random_briggs_graph(n, m): """Return the random graph G_{n,m}. Gives a graph picked randomly out of the set of all graphs with n nodes and m edges. Parameters ---------- n : int The number of nodes. m : int The number of edges. Notes ----- Algorithm by Keith M. Briggs Mar 31, 2006. Inspired by Knuth's Algorithm S (Selection sampling technique), in section 3.4.2 of References ---------- .. [1] Donald E. Knuth, The Art of Computer Programming, Volume 2 / Seminumerical algorithms Third Edition, Addison-Wesley, 1997. """ mmax = n * (n - 1) / 2 if m >= mmax: G = complete_graph(n) else: G = Graph() G + n if n == 1 or m >= mmax: return G u = 0 v = 1 t = 0 k = 0 while True: if random.randrange(mmax - t) < m - k: G.add_edge(u, v) k += 1 if k == m: return G t += 1 v += 1 if v == n: # go to next row of adjacency matrix u += 1 v = u + 1
def prepare_grid(G): # ensure that k is odd if len(G) % 2 == 0: G.add_named_vertex('dummykcol') for v in G.vertices - {'dummykcol'}: G.add_edge('dummykcol', v) H = Graph() # Create the color blue H.add_named_vertex('b') H.add_named_vertex('g') H.add_edge('b', 'g') return G, H
def random_planar_graph(n, m): G = Graph() for _v in xrange(n): G.add_vertex() Edges = get_maximal_planar_edges(G, n, 0) for _i in xrange(m): pos = random.randint(0, len(Edges) - 1) G.add_edge(Edges[pos][0], Edges[pos][1]) del Edges[pos] return G
def load_from_edge_list_named(strFileName, G = None): with open(strFileName, 'r') as f: lines = f.readlines() if G is None: G = Graph() for line in lines: if len(line) == 0 or line == '\n': continue fields = line.split() if not len(fields): continue if fields[0] == 'e': u, v = nvertex(fields[1]), nvertex(fields[2]) if u not in V(G): G.add_named_vertex(u) if v not in V(G): G.add_named_vertex(v) G.add_edge(u, v) G.set_vertex_index() return G
def reduction_from_kcol_to_3col(G, k): # add the main gadget T = lambda *x: "dummy(" + ",".join(map(str, x)) + ')' V = lambda v, c: str(v) + '(' + str(c) + ')' if k == 3: return G H = Graph() # Create the color blue H.add_named_vertex('c1') H.add_named_vertex('c2') H.add_named_vertex('c3') H.add_edge('c1', 'c2') H.add_edge('c1', 'c3') H.add_edge('c2', 'c3') # add vertices for v in G: H.add_named_vertex(V(v, 0)) H.add_edge(V(v, 0), 'c1') H.add_edge(V(v, 0), 'c3') H.add_named_vertex(V(v, k)) H.add_edge(V(v, k), 'c2') H.add_edge(V(v, k), 'c3') for i in range(1, k): H.add_named_vertex(V(v, i)) H.add_edge('c3', V(v, i)) for u, v in G.edges: for i in range(1, k + 1): H.add_named_vertex(T(u, v, u, i)) H.add_edge(V(u, i - 1), T(u, v, u, i)) H.add_edge(V(u, i), T(u, v, u, i)) H.add_named_vertex(T(u, v, v, i)) H.add_edge(V(v, i - 1), T(u, v, v, i)) H.add_edge(V(v, i), T(u, v, v, i)) H.add_edge(T(u, v, u, i), T(u, v, v, i)) H.set_vertex_index() return H
def reduce_3sat_to_3col(instance, G = None): """reduces a 3sat instance to a graph 3-coloring instance receives a graph G for each clause (a,b,c) gadget: (-a)----(a)---(g1) | \ | (g3)---(g4) (X) | / | \ / | (-b)----(b)---(g2) | (T) | | / \ | (-c)----(c)-------------(g5) (F) X is adjacent to all variables """ G = Graph() if G is None else G # add common gadget G.add_named_vertex('T') G.add_named_vertex('F') G.add_named_vertex('X') G.add_edge('T', 'F') G.add_edge('F', 'X') G.add_edge('X', 'T') # add gadget for variables variables = sorted(set([abs(v) for clause in instance for v in clause])) for v in variables: G.add_named_vertex(v) G.add_named_vertex(-v) G.add_edge('X', v) G.add_edge('X', -v) G.add_edge(v, -v) G.set_vertex_index(max(variables) + 1) # add the clause gadgets for a, b, c in instance: g1, g2, g3, g4, g5 = [G.add_vertex() for _i in range(5)] # triangle 1,2,3 G.add_edge(g1, g2) # 1 G.add_edge(g2, g3) # 2 G.add_edge(g3, g1) # 3 # bridge betwen triangle 1,2,3T and 4,5,T G.add_edge(g3, g4) # 4 # triangle 3,4,5 G.add_edge(g4, g5) # 5 G.add_edge(g5, 'T') # 6 G.add_edge('T', g4) # 7 # edges for clause a,b,c G.add_edge(a, g1) # 8 G.add_edge(b, g2) # 9 G.add_edge(c, g5) # 10 return G