NetworkX / Python_igraph：两个节点之间的所有路径，受节点列表限制

Question

我正在使用here的函数：

def find_all_paths(graph, start, end, mode = 'OUT', maxlen = None):
def find_all_paths_aux(adjlist, start, end, path, maxlen = None):
    path = path + [start]
    if start == end:
        return [path]
    paths = []
    if maxlen is None or len(path) <= maxlen:
        for node in adjlist[start] - set(path):
            paths.extend(find_all_paths_aux(adjlist, node, end, path, maxlen))
    return paths
adjlist = [set(graph.neighbors(node, mode = mode)) \
    for node in xrange(graph.vcount())]
all_paths = []
start = start if type(start) is list else [start]
end = end if type(end) is list else [end]
for s in start:
    for e in end:
        all_paths.extend(find_all_paths_aux(adjlist, s, e, [], maxlen))
return all_paths

查找两个节点之间的所有路径。

另一种功能是here：

def find_all_paths(graph, start, end):
path  = []
paths = []
queue = [(start, end, path)]
while queue:
    start, end, path = queue.pop()
    print 'PATH', path

    path = path + [start]
    if start == end:
        paths.append(path)
    for node in set(graph[start]).difference(path):
        queue.append((node, end, path))
return paths

我想扩展其中一个函数以获取另一个参数，即“via_nodes”列表。

如果路径在其结束和开始节点之间有这些 via_nodes 之一，则不应返回。

首先使用函数计算所有路径很容易，然后排除满足上述条件的路径，但为了提高性能，我希望它在遇到路径搜索时停止via_node 在早期阶段。

有什么想法吗？

Answer 1

您可以创建一个仅包含您希望在路径中看到的节点的子图 在 Networkx 2.5 中：

sub_graph = nx.subgraph_view(graph, filter_node:lambda n: n in [start, end] or n not in vn)
return all_simple_paths(sub_graph, start, end)

这将找到所有简单路径并排除 vn 中的任何节点，因为它们不在子图中

Answer 2

好的，我会回答自己，但会很高兴测试和 cmets：从上面的第二个函数（适用于 python-igraph 和 networkx），我添加了 vn 参数，所以路径搜索停止如果 a到达 vn 节点：

import igraph as ig

def find_all_paths2(graph, start, end, vn = []):
        """ 
        Finds all paths between nodes start and end in graph.
        If any node on such a path is within vn, the path is not         
        returned.
        !! start and end node can't be in the vn list !!

        Params:
        --------

        G : igraph graph

        start: start node index

        end : end node index

        vn : list of via- or stop-nodes indices

        Returns:
        --------

        A list of paths (node index lists) between start and end node
        """

    vn = vn if type(vn) is list else [vn]
    path  = []
    paths = []
    queue = [(start, end, path)]
    while queue:
        start, end, path = queue.pop()
        #print 'PATH', path
        path = path + [start]
        #print 'PATH after adding start ', path

        if start in vn:
            print start,' is in vianodes ',str(vn)
            pass#paths.append(path)

        if start == end:
            print 'end'
            paths.append(path)
        #print graph.neighbors(start)
        if start not in vn:
            print start,' not in vianodes ',str(vn)
            for node in set(graph.neighbors(start)).difference(path):
                queue.append((node, end, path))
    return paths

G = ig.Graph()
G.add_vertices(14)
G.add_edges([(13,10),(12,13),(11,12),(10,11),(9,10),(2,9),(0,1), (1,2),(2,3),(3,0),(0,4),(4,5),(5,6),(6,7),(7,8),(8,6)])#,(0,0)])
#G = G.as_directed()


for p in find_all_paths2(G,0,12,[]):
    print 'path: ',p

path:  [0, 3, 2, 9, 10, 13, 12]
path:  [0, 3, 2, 9, 10, 11, 12]
path:  [0, 1, 2, 9, 10, 13, 12]
path:  [0, 1, 2, 9, 10, 11, 12]

for p in find_all_paths2(G,0,12,[13]):
        print 'path: ',p


path:  [0, 3, 2, 9, 10, 11, 12]
path:  [0, 1, 2, 9, 10, 11, 12]

Answer 3

在长路径递归之前从图中删除节点。

完成后将它们放回去。

这在高度连接的图中占用更少的内存。

import networkx
G = networkx.Graph()
G.add_node(14)
G.add_edges_from([(13,10),(12,13),(11,12),(10,11),(9,10),(2,9),(0,1),(1,2),(2,3),(3,0),(0,4),(4,5),(5,6),(6,7),(7,8),(8,6)])


def simple_paths_with_node_exclusion(G, source, target, exclude_nodes):
        edge_list = []
        edge_list.extend(G.edges_iter(exclude_nodes))
        G.remove_nodes_from(exclude_nodes)
        value = networkx.all_simple_paths(G, source, target)
        G.add_nodes_from(edge_list)
        return value

print(list(simple_paths_with_node_exclusion(G,0,12,[13])))

• 如果您要进行时间或记忆力测试，我会很高兴听到下面 cmets 中真实数据的结果。