Graphs

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2023-12-01

图形是一组对象的图形表示，其中一些对象通过链接连接。互连对象由称为顶点的点表示，连接顶点的链接称为边。在这里的教程中非常详细地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。

Display graph vertices
Display graph edges
Add a vertex
Add an edge
创建图表

使用python词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，顶点之间的连接也称为边，作为字典中的值。

看看下面的图表 -

在上图中

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

我们可以在python程序中呈现此图形，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)

执行上述代码时，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())

执行上述代码时，会产生以下结果 -

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

显示图形边缘

找到图形边缘比顶点更小，因为我们必须找到在它们之间具有边缘的每对顶点。因此，我们创建一个空的边列表，然后迭代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())

执行上述代码时，会产生以下结果 -

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

添加顶点

添加顶点是直接的，我们在图表字典中添加另一个附加键。

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())

执行上述代码时，会产生以下结果 -

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

添加边缘

将边添加到现有图包括将新顶点视为元组并验证边是否已存在。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())

执行上述代码时，会产生以下结果 -

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