要创建一个新图\(G'\)，满足条件(a)、(b)和©，可以采取以下步骤：

1. 使用强连通分量算法（例如Tarjan算法）对图\(G\)进行处理，找到所有的强连通分量。记为\(SCC_1, SCC_2, \ldots, SCC_k\)。

2. 构建一个空的图\(G'\)，其中顶点集合与原始图\(G\)相同。

3. 遍历每个强连通分量\(SCC_i\)，若该分量只包含一个节点，则在\(G'\)中添加该节点。 否则，在\(G'\)中添加一个虚拟节点代表该强连通分量，并将该虚拟节点与分量内的所有实际节点连接起来。

4. 对于原始图中的每条边\((u,v)\)，若边所连接的两个顶点属于不同的强连通分量，则在\(G'\)中添加一条边从源强连通分量指向目标强连通分量。

这样构造得到的图\(G'\)满足条件(a)、(b)和©，即与原始图具有相同的强连通分量和分量图，并且所包含的边尽可能少。

以下是用Go语言实现上述算法的示例代码：

package main

import (
	"fmt"
)

type Graph struct {
	vertices []int
	edges    map[int][]int
}

func NewGraph() *Graph {
	return &Graph{
		vertices: []int{},
		edges:    make(map[int][]int),
	}
}

func (g *Graph) AddVertex(v int) {
	g.vertices = append(g.vertices, v)
}

func (g *Graph) AddEdge(u, v int) {
	g.edges[u] = append(g.edges[u], v)
}

type SCC struct {
	index        int
	lowlink      map[int]int
	onStack      map[int]bool
	stack        []int
	sccComponents [][]int
}

func NewSCC(graph *Graph) *SCC {
	return &SCC{
		index:        0,
		lowlink:      make(map[int]int),
		onStack:      make(map[int]bool),
		stack:        []int{},
		sccComponents: [][]int{},
	}
}

func (scc *SCC) TarjanAlgorithm(graph *Graph) [][]int {
	for _, v := range graph.vertices {
		if scc.lowlink[v] == 0 {
			scc.strongConnect(v, graph)
		}
	}
	return scc.sccComponents
}

func (scc *SCC) strongConnect(v int, graph *Graph) {
	scc.index++
	scc.lowlink[v] = scc.index
	scc.stack = append(scc.stack, v)
	scc.onStack[v] = true

	for _, w := range graph.edges[v] {
		if scc.lowlink[w] == 0 { // w has not yet been visited
			scc.strongConnect(w, graph)
			scc.lowlink[v] = min(scc.lowlink[v], scc.lowlink[w])
		} else if scc.onStack[w] { // w is in the current SCC being built
			scc.lowlink[v] = min(scc.lowlink[v], scc.lowlink[w])
		}
	}

	if scc.lowlink[v] == scc.index {
		component := []int{}
		w := -1
		for w != v {
			w, scc.stack = scc.stack[len(scc.stack)-1], scc.stack[:len(scc.stack)-1]
			scc.onStack[w] = false
			component = append(component, w)
		}
		scc.sccComponents = append(scc.sccComponents, component)
	}
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func buildNewGraph(graph *Graph, sccComponents [][]int) *Graph {
	newGraph := NewGraph()

	nodeMap := make(map[int]int)

	for i, component := range sccComponents {
		if len(component) > 1 { // Create virtual node for the SCC
			virtualNode := -i - 1
			nodeMap[virtualNode] = virtualNode
			newGraph.AddVertex(virtualNode)

			for _, node := range component {
				nodeMap[node] = virtualNode

				for _, neighbor := range graph.edges[node] {
					if nodeMap[neighbor] != virtualNode { // Add inter-component edge
						newGraph.AddEdge(virtualNode, neighbor)
					}
				}
			}
		} else { // Component with single node
			nodeMap[component[0]] = component[0]
			newGraph.AddVertex(component[0])
		}
		
    }

    for u, neighbors := range graph.edges { // Add intra-component edges within SCCs in new graph
        for _, v := range neighbors {
            if nodeMap[u] != nodeMap[v] { // Edge between different components in original graph 
                newGraph.AddEdge(nodeMap[u], nodeMap[v]) // Add edge in new graph
            }
        }
    }

    return newGraph
}

func main() {
	// 构建原始图
	graph := NewGraph()
	graph.AddVertex(1)
	graph.AddVertex(2)
	graph.AddVertex(3)
	graph.AddVertex(4)
	graph.AddVertex(5)
	graph.AddEdge(1, 2)
	graph.AddEdge(2, 3)
	graph.AddEdge(3, 1)
	graph.AddEdge(4, 2)
	graph.AddEdge(4, 5)

	// 使用Tarjan算法获取强连通分量
	scc := NewSCC(graph)
	sccComponents := scc.TarjanAlgorithm(graph)

	// 构建新图
	newGraph := buildNewGraph(graph, sccComponents)

	fmt.Println("Original Graph:")
	fmt.Println("Vertices:", graph.vertices)
	fmt.Println("Edges:", graph.edges)

	fmt.Println("\nNew Graph:")
	fmt.Println("Vertices:", newGraph.vertices)
	fmt.Println("Edges:", newGraph.edges)
}

这段代码首先定义了一个Graph结构来表示图，包含顶点和边的信息。然后定义了一个SCC结构来实现Tarjan算法进行强连通分量的计算。接着使用上述步骤中的算法来创建新图\(G'\)，并最终输出结果。

希望以上代码可以帮助到您！


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