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📜  Python图形

📅  最后修改于: 2020-11-07 08:39:31             🧑  作者: Mango

图形是一组对象的图形表示，其中一些对象对通过链接连接。相互连接的对象由称为顶点的点表示，而连接这些顶点的链接称为边。与图形相关的各种术语和功能在此处的教程中进行了详细描述。在本章中，我们将了解如何使用Python程序创建图形并向其中添加各种数据元素。以下是我们在图形上执行的基本操作。

  • 显示图顶点
  • 显示图形边缘
  • 添加一个顶点
  • 添加边缘
  • 创建图

使用Python字典数据类型可以轻松呈现图形。我们将顶点表示为字典的键，并且将顶点之间的连接也称为边作为字典中的值。

看一下下图-

数组声明

在上图中

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

我们可以在Python程序中显示此图，如下所示。

# 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)

执行以上代码后，将产生以下结果-

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

显示图顶点

为了显示图顶点，我们简单地找到图字典的键。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())

执行以上代码后，将产生以下结果-

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

显示图形边缘

查找图的边缘比顶点要难得多，因为我们必须找到在一对顶点之间具有边的一对顶点。因此，我们创建了一个空的边列表，然后再遍历与每个顶点关联的边值。形成一个列表，其中包含从顶点找到的不同边缘组。

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())

执行以上代码后，将产生以下结果-

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

添加一个顶点

直接添加顶点是在图字典中添加另一个键的过程。

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())

执行以上代码后，将产生以下结果-

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

添加边缘

将边缘添加到现有图形涉及将新顶点视为元组，并验证边缘是否已存在。如果没有，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())

执行以上代码后，将产生以下结果-

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