标题：Python - 图形

图表是一组对象通过链接连接的一组对象的图形表示。互连对象由称为顶点的点表示，连接顶点的链接称为边。我们的教程在这里详细描述了与图形相关的各种术语和功能。在本章中，我们将看到如何使用python程序创建图形并向其添加各种数据元素。以下是我们在图表上执行的基本操作。

• 显示图形顶点
• 显示图形边缘
• 添加一个顶点
• 添加边缘
• 创建一个图

可以使用python字典数据类型轻松呈现图形。我们将顶点表示为字典的关键字，顶点之间的连接也称为边界，作为字典中的值。

看看下面的图表 -

在上面的图中

V = {a, b, c, d, e}
E = {ab, ac, bd, cd, de}

我们可以在下面的python程序中展示这个图。

# Create the dictionary with graph elements
graph = { "a" : ["b","c"],
          "b" : ["a", "d"],
          "c" : ["a", "d"],
          "d" : ["e"],
          "e" : ["d"]
         }

# Print the graph        
print(graph)

当上面的代码被执行时，它会产生以下结果 -

{'c': ['a', 'd'], 'a': ['b', 'c'], 'e': ['d'], 'd': ['e'], 'b': ['a', 'd']}

显示图形顶点

为了显示图形顶点，我们简单地找到图形字典的关键字。我们使用keys（）方法。

class graph:
    def __init__(self,gdict=None):
        if gdict is None:
            gdict = []
        self.gdict = gdict

# Get the keys of the dictionary
    def getVertices(self):
        return list(self.gdict.keys())

# Create the dictionary with graph elements
graph_elements = { "a" : ["b","c"],
                "b" : ["a", "d"],
                "c" : ["a", "d"],
                "d" : ["e"],
                "e" : ["d"]
                }

g = graph(graph_elements)

print(g.getVertices())

当上面的代码被执行时，它会产生以下结果 -

['d', 'b', 'e', 'c', 'a']

显示图形边缘

寻找图形边缘比顶点少一些，因为我们必须找到每对顶点之间的边缘。因此，我们创建一个空边列表，然后迭代与每个顶点关联的边值。一个列表形成了包含从顶点找到的不同组的边。

class graph:

    def __init__(self,gdict=None):
        if gdict is None:
            gdict = {}
        self.gdict = gdict

    def edges(self):
        return self.findedges()
# Find the distinct list of edges

    def findedges(self):
        edgename = []
        for vrtx in self.gdict:
            for nxtvrtx in self.gdict[vrtx]:
                if {nxtvrtx, vrtx} not in edgename:
                    edgename.append({vrtx, nxtvrtx})
        return edgename

# Create the dictionary with graph elements
graph_elements = { "a" : ["b","c"],
                "b" : ["a", "d"],
                "c" : ["a", "d"],
                "d" : ["e"],
                "e" : ["d"]
                }

g = graph(graph_elements)

print(g.edges())

当上面的代码被执行时，它会产生以下结果 -

[{'b', 'a'}, {'b', 'd'}, {'e', 'd'}, {'a', 'c'}, {'c', 'd'}]

添加一个顶点

添加一个顶点是直接向我们添加另一个关键字到图形字典。

class graph:

  def __init__(self,gdict=None):
      if gdict is None:
          gdict = {}
      self.gdict = gdict

  def getVertices(self):
      return list(self.gdict.keys())

# Add the vertex as a key
  def addVertex(self, vrtx):
     if vrtx not in self.gdict:
          self.gdict[vrtx] = []

# Create the dictionary with graph elements
graph_elements = { "a" : ["b","c"],
              "b" : ["a", "d"],
              "c" : ["a", "d"],
              "d" : ["e"],
              "e" : ["d"]
              }

g = graph(graph_elements)

g.addVertex("f")

print(g.getVertices())

当上面的代码被执行时，它会产生以下结果 -

['f', 'e', 'b', 'a', 'c','d']

添加边缘

将边添加到现有图涉及将新顶点视为元组并验证边是否已经存在。如果不是，则添加边缘。

class graph:

    def __init__(self,gdict=None):
        if gdict is None:
            gdict = {}
        self.gdict = gdict

    def edges(self):
        return self.findedges()
# Add the new edge

    def AddEdge(self, edge):
        edge = set(edge)
        (vrtx1, vrtx2) = tuple(edge)
        if vrtx1 in self.gdict:
            self.gdict[vrtx1].append(vrtx2)
        else:
            self.gdict[vrtx1] = [vrtx2]

# List the edge names
    def findedges(self):
        edgename = []
        for vrtx in self.gdict:
            for nxtvrtx in self.gdict[vrtx]:
                if {nxtvrtx, vrtx} not in edgename:
                    edgename.append({vrtx, nxtvrtx})
        return edgename

# Create the dictionary with graph elements
graph_elements = { "a" : ["b","c"],
                "b" : ["a", "d"],
                "c" : ["a", "d"],
                "d" : ["e"],
                "e" : ["d"]
                }

g = graph(graph_elements)
g.AddEdge({'a','e'})
g.AddEdge({'a','c'})
print(g.edges())

当上面的代码被执行时，它会产生以下结果 -

[{'e', 'd'}, {'b', 'a'}, {'b', 'd'}, {'a', 'c'}, {'a', 'e'}, {'c', 'd'}]