以下是一个示例代码，用于按最短路径排序并不排除断开的节点：

import heapq

def shortest_path(graph, start):
    # 初始化距离字典和前驱节点字典
    distances = {node: float('inf') for node in graph}
    distances[start] = 0
    previous_nodes = {node: None for node in graph}
    
    # 使用堆优化的Dijkstra算法计算最短路径
    heap = [(0, start)]
    while heap:
        current_distance, current_node = heapq.heappop(heap)
        
        # 跳过已经处理过的节点
        if current_distance > distances[current_node]:
            continue
        
        # 遍历当前节点的邻居节点
        for neighbor, weight in graph[current_node].items():
            distance = current_distance + weight
            
            # 更新距离和前驱节点
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                previous_nodes[neighbor] = current_node
                heapq.heappush(heap, (distance, neighbor))
    
    return distances, previous_nodes

def sort_by_shortest_path(graph, start):
    # 调用最短路径函数获取距离字典和前驱节点字典
    distances, previous_nodes = shortest_path(graph, start)
    
    # 按距离排序节点
    sorted_nodes = sorted(distances.keys(), key=lambda x: distances[x])
    
    return sorted_nodes

# 测试示例
graph = {
    'A': {'B': 5, 'C': 2},
    'B': {'A': 5, 'D': 1},
    'C': {'A': 2, 'D': 6},
    'D': {'B': 1, 'C': 6}
}

start_node = 'A'
sorted_nodes = sort_by_shortest_path(graph, start_node)
print(sorted_nodes)

输出结果为：['A', 'C', 'B', 'D']，表示按最短路径排序的节点顺序。