################################################################################ # # This file is part of Gato (Graph Animation Toolbox) # # file: Graph.py # author: Alexander Schliep (schliep@molgen.mpg.de) # # Copyright (C) 1998-2005, Alexander Schliep, Winfried Hochstaettler and # Copyright 1998-2001 ZAIK/ZPR, Universitaet zu Koeln # # Contact: schliep@molgen.mpg.de, wh@zpr.uni-koeln.de # # Information: http://gato.sf.net # # This library is free software; you can redistribute it and/or # modify it under the terms of the GNU Library General Public # License as published by the Free Software Foundation; either # version 2 of the License, or (at your option) any later version. # # This library is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # Library General Public License for more details. # # You should have received a copy of the GNU Library General Public # License along with this library; if not, write to the Free # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA # # # # This file is version $Revision: 1.27 $ # from $Date: 2006/01/18 13:00:41 $ # last change by $Author: schliep $. # ################################################################################ from GatoGlobals import * from DataStructures import Point2D, VertexLabeling, EdgeLabeling, EdgeWeight #from math import log import logging log = logging.getLogger("Graph.py") ################################################################################ # # Graph # ################################################################################ class Graph: """ Provides a mathematical graph object consisting of vertices and (directed) edges connecting those vertices. Graphs have - a labeling for vertices allowing to specify names - an embedding of vertices into 2D-space - one or more sets of edge weights Vertices are specified via id (integer number) and edges via (tail,head)-tuples NOTE: ids are supposed to be consecutive and ranging from 0 to G.Order() - 1 !!! Use the labeling to *display* other numbers for vertices. At least one set of edge weights is assumed to exist and accessible as self.edgeWeights[0]; self.euclidian and Euclidify refer to this self.edgeWeights[0] """ def __init__(self): self.simple = 1 self.euclidian = 1 self.directed = 0 self.vertices = [] self.adjLists = {} self.invAdjLists = {} # Inverse Adjazenzlisten self.highVertexID = 0 # INTERNAL self.embedding = VertexLabeling() # 2D-Positions self.labeling = VertexLabeling() # Names of vertices self.edgeWeights = {} # Dictionary of edge labellings self.edgeWeights[0] = EdgeWeight(self) self.vertexWeights = {} # None by default self.size = 0 self.edgeWidth = None self.vertexAnnotation = None self.edgeAnnotation = None self.properties = {} def AddVertex(self): """ Add an isolated vertex. Returns the id of the new vertex """ id = self.GetNextVertexID() self.vertices.append(id) self.adjLists[id] = [] self.invAdjLists[id] = [] return id def DeleteVertex(self, v): """ Delete the vertex v and its incident edges """ outVertices = self.OutNeighbors(v)[:] # Need a copy here inVertices = self.InNeighbors(v)[:] for w in outVertices: self.DeleteEdge(v,w) for w in inVertices: if w != v: # We have already deleted loops self.DeleteEdge(w,v) self.vertices.remove(v) #self.adjLists[v] = None #self.invAdjLists[v] = None # XXX Should clean up all other stuff too ... def QVertex(self, v): """ Check whether v is a vertex """ return v in self.vertices def AddEdge(self,tail,head): """ Add an edge (tail,head). Returns nothing Raises GraphNotSimpleError if - trying to add a loop - trying to add an edge multiply In case of directed graphs (tail,head) and (head,tail) are distinct edges """ if self.simple == 1 and tail == head: # Loop raise GraphNotSimpleError, '(%d,%d) is a loop' % (tail,head) if self.directed == 0 and tail in self.adjLists[head]: raise GraphNotSimpleError, '(%d,%d) is already an undirected edge' % (head,tail) if head in self.adjLists[tail]: # Multiple edge raise GraphNotSimpleError, '(%d,%d) is already an directed edge' % (tail,head) self.adjLists[tail].append(head) self.invAdjLists[head].append(tail) self.size = self.size + 1 def DeleteEdge(self,tail,head): """ Deletes edge (tail,head). Does *not* handle undirected graphs implicitely. Raises NoSuchEdgeError upon error. """ try: self.adjLists[tail].remove(head) self.invAdjLists[head].remove(tail) self.size = self.size - 1 except KeyError: raise NoSuchEdgeError, "(%d,%d) is not an edge." % (tail,head) def Edge(self,tail,head): """ Handles undirected graphs by return correct ordered vertices as (tail,head). Raises NoSuchEdgeError upon error. """ if tail not in self.vertices or head not in self.vertices: raise NoSuchEdgeError, "(%d,%d) is not an edge." % (tail,head) if head in self.adjLists[tail]: return (tail,head) elif self.directed == 0 and tail in self.adjLists[head]: return (head,tail) else: raise NoSuchEdgeError, "(%d,%d) is not an edge." % (tail,head) def QEdge(self,tail,head): """ Returns 1 if (tail,head) is an edge in G. If G is undirected order of vertices does not matter """ if self.directed == 1: return head in self.adjLists[tail] else: return (head in self.adjLists[tail]) or (tail in self.adjLists[head]) def QEdgeWidth(self): """ Returns 1 if individual edge widths are defined, 0 else """ return self.edgeWidth != None def EdgeWidth(self, tail, head): return self.edgeWidth[(tail,head)] def Neighborhood(self,v): """ Returns the vertices which are connected to v. Does handle undirected graphs (i.e., returns vertices w s.t. either (v,w) or (w,v) is an edge) """ if self.directed: return self.OutNeighbors(v) else: return self.InOutNeighbors(v) def InNeighbors(self,v): """ Returns vertices w for which (w,v) is an edge """ return self.invAdjLists[v] def OutNeighbors(self,v): """ Returns vertices w for which (v,w) is an edge """ return self.adjLists[v] def InOutNeighbors(self,v): """ Returns vertices w for which (v,w) or (w,v) is an edge """ return self.InNeighbors(v) + self.OutNeighbors(v) def InEdges(self,v): """ Returns edges (*,v) """ f = lambda x, vertex = v : (x,vertex) return map(f, self.invAdjLists[v]) def OutEdges(self,v): """ Returns edges (v,*) """ f = lambda x, vertex = v : (vertex,x) return map(f ,self.adjLists[v]) def IncidentEdges(self,v): """ Returns edges (v,*) and (*,v) """ return self.InEdges(v) + self.OutEdges(v) def Edges(self): """ Returns all edges """ tmp = [] for v in self.vertices: tmp = tmp + self.OutEdges(v) return tmp def Vertices(self): """ Returns all edges """ return self.vertices def printMy(self): """ Debugging only """ for v in self.vertices: print v, " -- ", self.adjLists[v] def GetNextVertexID(self): """ *Internal* returns next free vertex id """ self.highVertexID = self.highVertexID + 1 return self.highVertexID def Order(self): """ Returns order i.e., the number of vertices """ return len(self.vertices) def Size(self): """ Returns size i.e., the number of edge """ return self.size def Degree(self, v): """ Returns the degree of the vertex v, which is - the number of incident edges in the undirect case - the number of outgoing edges in the directed case """ if self.directed: return len(self.adjLists[v]) else: return len(self.adjLists[v]) + len(self.invAdjLists[v]) def InDegree(self, v): """ Returns the number of incoming edges for direct graphs """ if self.directed: return len(self.invAdjLists[v]) else: return None # Proper error to raise? def OutDegree(self, v): """ Returns the number of incoming edges for direct graphs """ if self.directed: return len(self.adjLists[v]) else: return None # Proper error to raise? def QEuclidian(self): """ Returns 1 if the graph is euclidian, 0 else """ return self.euclidian def QDirected(self): """ Returns 1 if the graph is directed, 0 else """ return self.directed def CalculateWidthFromWeight(self, scale, weightID = 0): """ Calculate width of edges (self.edgeWidth will be used by GraphDisplay if not none) from the specified set of edge weights. Default: weightID = 0 is used """ self.edgeWidth = EdgeLabeling() edges = self.Edges() maxWeight = max(self.edgeWeights[weightID].label.values()) for e in edges: self.edgeWidth[e] = scale * (1 + 35 * self.edgeWeights[weightID][e] / maxWeight) def NrOfEdgeWeights(self): return len(self.edgeWeights.keys()) def SetEdgeWeight(self,i,v,w,value): self.edgeWeights[i][(v,w)] = value def GetEdgeWeight(self,i,v,w): return self.edgeWeights[i][(v,w)] def NrOfVertexWeights(self): return len(self.vertexWeights.keys()) def SetVertexWeight(self,i,v,value): self.vertexWeights[i][v] = value def GetVertexWeight(self,i,v): return self.vertexWeights[i][v] def GetLabeling(self,v): return self.labeling[v] def SetLabeling(self,v, value): self.labeling[v] = value def GetEmbedding(self,v): return self.embedding[v] def SetEmbedding(self,v, x, y): self.embedding[v] = Point2D(x,y) def Euclidify(self): """ Replace edge weights with weightID = 0 with Euclidean distance between incident vertices """ for v in self.vertices: for w in self.adjLists[v]: d = ((self.embedding[v].x - self.embedding[w].x)**2 + (self.embedding[v].y - self.embedding[w].y)**2)**(.5) if self.edgeWeights[0].QInteger(): self.edgeWeights[0][(v,w)] = int(round(d)) else: self.edgeWeights[0][(v,w)] = d self.euclidian = 1 def Integerize(self, weightID = 0): """ Integerize: Make all edge weights integers """ if weightID == 'all': for w in self.edgeWeights.keys(): self.edgeWeights[w].Integerize() else: self.edgeWeights[weightID].Integerize() def Undirect(self): """ If (u,v) and (v,u) are edges in the directed graph, remove one of them. to make graph undirected (no multiple edges allowed). Which one gets deleted depends on ordering in adjacency lists. """ if not self.directed: return for v in self.vertices: for w in self.adjLists[v]: if v in self.adjLists[w]: self.DeleteEdge(w,v) self.directed = 0 def SetProperty(self, name, val): """ Set the value of property 'name' to 'val' """ self.properties[name] = val def Property(self,name): """ Return the value of property 'name'. If the property 'name' has not been set 'Unknown' is returned """ try: return self.properties[name] except: return 'Unknown' def About(self): """ Return string containing HTML code providing information about the graph """ return "

No information available

" ################################################################################ # # Induced Subgraph # ################################################################################ class SubGraph(Graph): """ Provides a subgraph, i.e., a subset of the vertices and edges of a specified graph Vertices are specified via ids from its supergraph and edges via (tail,head)-tuples It also keeps track of the subgraphs total weight (= sum of edge weights) for weights with weightID == 0 """ def __init__(self,G): Graph.__init__(self) self.superGraph = G self.embedding = self.superGraph.embedding self.labeling = self.superGraph.labeling self.edgeWeights = self.superGraph.edgeWeights self.directed = self.superGraph.directed self.totalWeight = 0 def AddVertex(self,v): """ Add a vertex from the supergraph to the subgraph. Returns NoSuchVertexError if v does not exist in supergraph """ try: self.vertices.append(v) #f = lambda x, vertexList=self.vertices: x in vertexList #self.adjLists[v] = filter(f, self.superGraph.adjLists[v]) #self.invAdjLists[v] = filter(f, self.superGraph.invAdjLists[v]) self.adjLists[v] = [] self.invAdjLists[v] = [] except: raise NoSuchVertexError, "%d is not a vertex in the supergraph" % v def AddEdge(self,tail,head): """ Add an edge from the supergraph to the subgraph. Will also add tail and/or head if there are not already in subgraph """ try: if not tail in self.vertices: self.AddVertex(tail) if not head in self.vertices: self.AddVertex(head) (tail,head) = self.superGraph.Edge(tail,head) self.adjLists[tail].append(head) self.invAdjLists[head].append(tail) self.size = self.size + 1 try: w = self.superGraph.edgeWeights[0][(tail,head)] except KeyError: w = 0.0 # XXX we dont have w weight for the edge. Make totalWeight configurable/subclass self.totalWeight += w except (KeyError, NoSuchVertexError, NoSuchEdgeError): raise NoSuchEdgeError, "(%d,%d) is not an edge in the supergraph." % (tail,head) def AddSubGraph(self,G): """ Add subgraph G to self. Will do nothing if self and G have distinct supergraphs """ if self.superGraph != G.superGraph: log.error("AddSubGraph: distinct superGraphs") return for v in G.vertices: self.AddVertex(v) for e in G.Edges(): self.AddEdge(e[0],e[1]) def DeleteEdge(self,tail,head): """ Delete edge from subgraph. Raises NoSuchEdgeError upon error """ if tail in self.vertices and head in self.vertices: superEdge = self.superGraph.Edge(tail,head) self.totalWeight = self.totalWeight - self.superGraph.edgeWeights[0][superEdge] self.adjLists[tail].remove(head) self.invAdjLists[head].remove(tail) self.size = self.size - 1 else: raise NoSuchEdgeError, "(%d,%d) is not an edge." % (tail,head) def Clear(self): """ Delete all vertices and edges from the subgraph. """ self.vertices = [] self.adjLists = {} self.invAdjLists = {} # Inverse Adjazenzlisten self.size = 0 self.totalWeight = 0 def GetNextVertexID(self): """ *Internal* safeguard """ log.error("Induced Subgraph -> GetNextVertexID should never have been called") def Weight(self): """ Returns the total weight (= sum of edge weights) of subgraph """ return self.totalWeight def QEuclidian(self): """ Returns 1 if the super graph is euclidian, 0 else """ return self.superGraph.euclidian def QDirected(self): """ Returns 1 if the super graph is directed, 0 else""" return self.superGraph.directed def QEdge(self,tail,head): """ Returns 1 if (tail,head) is an edge in G """ if not tail in self.vertices or not head in self.vertices: return 0 if self.directed == 1: return head in self.adjLists[tail] else: return head in self.adjLists[tail] or tail in self.adjLists[head]