Is there a way to iterate over the nodes of a NetworkX DiGraph in order? The traversal methods I found iterate over edges rather than nodes, or require a source. In my case, my DAG has multiple sources. I don't really care in which order these sources are iterated over, as long as one node does not get processed before all of its ancestors have been processed.
I usually implement something like this:
import networkx as nx
G = nx.gnr_graph(100, 0.1)
root_node = list(G.nodes)[80]
children_next = set()
searched_nodes = set()
children_current = [root_node]
level = 0
while len(children_current) != 0:
for n in children_current:
searched_nodes.add(n)
for s in G.successors(n): #exchange with predecessors to get parents
children_next.add(s)
children_next = children_next.difference(searched_nodes)
children_current = list(children_next)
level += 1
print("root={}; level={}, successors={}".format(root_node, level, str(children_current)))
This allows me to travers the graph in a direction (exchange G.successors(n) with G.predecessors(n) to change the direction). It traverses the nodes of the graph according to their distance from the root node.
Related
I am currently working on a graph of twitter users, where I have 2 csv files, one is the node list with close to 147,000 nodes and the other is a edge list with all the relationships between the users.
When I import the files to networkx and use the info() method on the graph it tells me i have upwards of 5,000,000 nodes in the graph (The figure is similar if I use info() on both the directed and undirected version of the graph)
I have tried this with smaller datasets and the number of nodes matched the number in my node list file. Does anyone know why this may be happening?
many thanks
EDIT
The code I am using can be seen below
import csv
import networkx as nx
import pandas as pd
with open('node list.csv', 'r') as nodecsv: # Open the file
nodereader = csv.reader(nodecsv) # Read the csv
# Retrieve the data (using Python list comprhension and list slicing to remove the header row, see footnote 3)
nodes = [n for n in nodereader][1:]
node_names = [n[0] for n in nodes] # Get a list of only the node names
with open('edge list.csv', 'r') as edgecsv: # Open the file
edgereader = csv.reader(edgecsv) # Read the csv
edges = [tuple(e) for e in edgereader][1:] # Retrieve the data
print(len(node_names))
print(len(edges))
G = nx.Graph()
# G.add_nodes_from(node_names)
G.add_edges_from(edges)
print(nx.info(G))
print(total_nodes)
follower_count_dict = {}
friend_count_dict = {}
staus_count_dict = {}
created_at_dict = {}
for node in nodes: # Loop through the list, one row at a time
follower_count_dict[node[0]] = node[1]
friend_count_dict[node[0]] = node[2]
staus_count_dict[node[0]] = node[3]
created_at_dict[node[0]] = node[4]
#print( user_followers_count_dict)
nx.set_node_attributes(G, follower_count_dict, 'follower_count')
nx.set_node_attributes(G, friend_count_dict, 'friend_count')
nx.set_node_attributes(G, staus_count_dict, 'staus_count')
nx.set_node_attributes(G, created_at_dict, 'created_at')
DG = nx.DiGraph()
DG.add_nodes_from(node_names)
DG.add_edges_from(edges)
nx.set_node_attributes(DG, follower_count_dict, 'follower_count')
nx.set_node_attributes(DG, friend_count_dict, 'friend_count')
nx.set_node_attributes(DG, staus_count_dict, 'staus_count')
nx.set_node_attributes(DG, created_at_dict, 'created_at')
Snapshot of user list file
Snapshot of edge list file
Your edge list includes nodes that do not appear in your node list. So when those edges are added, networkx adds the nodes as well.
Reasons for this could include the nodes being treated as strings with different white space (perhaps '\n' at the end), or nodes being treated as integers in some cases and strings in others.
A way to deal with this is that before you add the edges, do a loop that checks whether each node is in the graph and if not, prints out the node:
for edge in edges:
for node in edge:
if node not in G:
print(node)
The idea is to compute resilience of the network presented as an undirected graph in form
{node: (set of its neighbors) for each node in the graph}.
The function removes nodes from the graph in random order one by one and calculates the size of the largest remaining connected component.
The helper function bfs_visited() returns the set of nodes that are still connected to the given node.
How can I improve the implementation of the algorithm in Python 2? Preferably without changing the breadth-first algorithm in the helper function
def bfs_visited(graph, node):
"""undirected graph {Vertex: {neighbors}}
Returns the set of all nodes visited by the algrorithm"""
queue = deque()
queue.append(node)
visited = set([node])
while queue:
current_node = queue.popleft()
for neighbor in graph[current_node]:
if neighbor not in visited:
visited.add(neighbor)
queue.append(neighbor)
return visited
def cc_visited(graph):
""" undirected graph {Vertex: {neighbors}}
Returns a list of sets of connected components"""
remaining_nodes = set(graph.keys())
connected_components = []
for node in remaining_nodes:
visited = bfs_visited(graph, node)
if visited not in connected_components:
connected_components.append(visited)
remaining_nodes = remaining_nodes - visited
#print(node, remaining_nodes)
return connected_components
def largest_cc_size(ugraph):
"""returns the size (an integer) of the largest connected component in
the ugraph."""
if not ugraph:
return 0
res = [(len(ccc), ccc) for ccc in cc_visited(ugraph)]
res.sort()
return res[-1][0]
def compute_resilience(ugraph, attack_order):
"""
input: a graph {V: N}
returns a list whose k+1th entry is the size of the largest cc after
the removal of the first k nodes
"""
res = [len(ugraph)]
for node in attack_order:
neighbors = ugraph[node]
for neighbor in neighbors:
ugraph[neighbor].remove(node)
ugraph.pop(node)
res.append(largest_cc_size(ugraph))
return res
I received this tremendously great answer from Gareth Rees, which covers the question completely.
Review
The docstring for bfs_visited should explain the node argument.
The docstring for compute_resilience should explain that the ugraph argument gets modified. Alternatively, the function could take a copy of the graph so that the original is not modified.
In bfs_visited the lines:
queue = deque()
queue.append(node)
can be simplified to:
queue = deque([node])
The function largest_cc_size builds a list of pairs:
res = [(len(ccc), ccc) for ccc in cc_visited(ugraph)]
res.sort()
return res[-1][0]
But you can see that it only ever uses the first element of each pair (the size of the component). So you could simplify it by not building the pairs:
res = [len(ccc) for ccc in cc_visited(ugraph)]
res.sort()
return res[-1]
Since only the size of the largest component is needed, there is no need to build the whole list. Instead you could use max to find the largest:
if ugraph:
return max(map(len, cc_visited(ugraph)))
else:
return 0
If you are using Python 3.4 or later, this can be further simplified using the default argument to max:
return max(map(len, cc_visited(ugraph)), default=0)
This is now so simple that it probably doesn't need its own function.
This line:
remaining_nodes = set(graph.keys())
can be written more simply:
remaining_nodes = set(graph)
There is a loop over the set remaining_nodes where on each loop iteration you update remaining_nodes:
for node in remaining_nodes:
visited = bfs_visited(graph, node)
if visited not in connected_components:
connected_components.append(visited)
remaining_nodes = remaining_nodes - visited
It looks as if the intention of the code to avoid iterating over the nodes in visited by removing them from remaining_nodes, but this doesn't work! The problem is that the for statement:
for node in remaining_nodes:
only evaluates the expression remaining_nodes once, at the start of the loop. So when the code creates a new set and assigns it to remaining_nodes:
remaining_nodes = remaining_nodes - visited
this has no effect on the nodes being iterated over.
You might imagine trying to fix this by using the difference_update method to adjust the set being iterated over:
remaining_nodes.difference_update(visited)
but this would be a bad idea because then you would be iterating over a set and modifying it within the loop, which is not safe. Instead, you need to write the loop as follows:
while remaining_nodes:
node = remaining_nodes.pop()
visited = bfs_visited(graph, node)
if visited not in connected_components:
connected_components.append(visited)
remaining_nodes.difference_update(visited)
Using while and pop is the standard idiom in Python for consuming a data structure while modifying it — you do something similar in bfs_visited.
There is now no need for the test:
if visited not in connected_components:
since each component is produced exactly once.
In compute_resilience the first line is:
res = [len(ugraph)]
but this only works if the graph is a single connected component to start with. To handle the general case, the first line should be:
res = [largest_cc_size(ugraph)]
For each node in attack order, compute_resilience calls:
res.append(largest_cc_size(ugraph))
But this doesn't take advantage of the work that was previously done. When we remove node from the graph, all connected components remain the same, except for the connected component containing node. So we can potentially save some work if we only do a breadth-first search over that component, and not over the whole graph. (Whether this actually saves any work depends on how resilient the graph is. For highly resilient graphs it won't make much difference.)
In order to do this we'll need to redesign the data structures so that we can efficiently find the component containing a node, and efficiently remove that component from the collection of components.
This answer is already quite long, so I won't explain in detail how to redesign the data structures, I'll just present the revised code and let you figure it out for yourself.
def connected_components(graph, nodes):
"""Given an undirected graph represented as a mapping from nodes to
the set of their neighbours, and a set of nodes, find the
connected components in the graph containing those nodes.
Returns:
- mapping from nodes to the canonical node of the connected
component they belong to
- mapping from canonical nodes to connected components
"""
canonical = {}
components = {}
while nodes:
node = nodes.pop()
component = bfs_visited(graph, node)
components[node] = component
nodes.difference_update(component)
for n in component:
canonical[n] = node
return canonical, components
def resilience(graph, attack_order):
"""Given an undirected graph represented as a mapping from nodes to
an iterable of their neighbours, and an iterable of nodes, generate
integers such that the the k-th result is the size of the largest
connected component after the removal of the first k-1 nodes.
"""
# Take a copy of the graph so that we can destructively modify it.
graph = {node: set(neighbours) for node, neighbours in graph.items()}
canonical, components = connected_components(graph, set(graph))
largest = lambda: max(map(len, components.values()), default=0)
yield largest()
for node in attack_order:
# Find connected component containing node.
component = components.pop(canonical.pop(node))
# Remove node from graph.
for neighbor in graph[node]:
graph[neighbor].remove(node)
graph.pop(node)
component.remove(node)
# Component may have been split by removal of node, so search
# it for new connected components and update data structures
# accordingly.
canon, comp = connected_components(graph, component)
canonical.update(canon)
components.update(comp)
yield largest()
In the revised code, the max operation has to iterate over all the remaining connected components in order to find the largest one. It would be possible to improve the efficiency of this step by storing the connected components in a priority queue so that the largest one can be found in time that's logarithmic in the number of components.
I doubt that this part of the algorithm is a bottleneck in practice, so it's probably not worth the extra code, but if you need to do this, then there are some Priority Queue Implementation Notes in the Python documentation.
Performance comparison
Here's a useful function for making test cases:
from itertools import combinations
from random import random
def random_graph(n, p):
"""Return a random undirected graph with n nodes and each edge chosen
independently with probability p.
"""
assert 0 <= p <= 1
graph = {i: set() for i in range(n)}
for i, j in combinations(range(n), 2):
if random() <= p:
graph[i].add(j)
graph[j].add(i)
return graph
Now, a quick performance comparison between the revised and original code. Note that we have to run the revised code first, because the original code destructively modifies the graph, as noted in §1.2 above.
>>> from timeit import timeit
>>> G = random_graph(300, 0.2)
>>> timeit(lambda:list(resilience(G, list(G))), number=1) # revised
0.28782312001567334
>>> timeit(lambda:compute_resilience(G, list(G)), number=1) # original
59.46968446299434
So the revised code is about 200 times faster on this test case.
I'm working in a project using the library Networkx ( for graph management ) in Python, and I been having trouble trying to implement what I need
I have a collection of directed graphs, holding special objects as nodes and weights associated with the edges, the thing is I need to go through the graph from output nodes to input nodes. and for each node I have to take the weights from their predecessors and an operation calculated by that predecessor node to build the operation form my output node. But the problem is that the operations of the predecessors may depend from their own predecessors, and so on, so I'm wondering how I can solve this problem.
So far I have try the next, lets say I have a list of my output nodes and I can go through the predecessors using the methods of the Networkx library:
# graph is the object containig my directe graph
for node in outputNodes:
activate_predecessors(node , graph)
# ...and a function to activate the predecessors ..
def activate_predecessors( node = None , graph ):
ws = [] # a list for the weight
res = [] # a list for the response from the predecessor
for pred in graph.predecessors( node ):
# get the weights
ws.append( graph[pred][node]['weight'] )
activate_predecessors( pred , graph )
res.append( pred.getResp() ) # append the response from my predecessor node to a list, but this response depend on their own predecessors, so i call this function over the current predecessor in a recursive way
# after I have the two lists ( weights and the response the node should calculate a reduce operation
# do after turning those lists into numpy arrays...
node.response = np.sum( ws*res )
This code seems to work... I tried it on in some random many times, but in many occasions it gives a maximum recursion depth exceeded so I need to rewrite it in a more stable ( and possibly iterative ) way in order to avoid maximum recursion. but I'm running out of ideas to handle this..
the library has some searching algorithms (Depth first search) but after I don't know how it could help me to solve this.
I also try to put some flags on the nodes to know if it had been already activated but I keep getting the same error.
Edit: I forgot, the input nodes have a defined response value so they don't need to do calculations.
your code may contain an infinite recursion if there is a cycle between two nodes. for example:
import networkx as nx
G = nx.DiGraph()
G.add_edges_from([(1,2), (2,1)])
def activate_nodes(g, node):
for pred in g.predecessors(node):
activate_nodes(g, pred)
activate_nodes(G, 1)
RuntimeError: maximum recursion depth exceeded
if you have possible cycles on one of the graphs you better mark each node as visited or change the edges on the graph to have no cycles.
assuming you do not have cycles on your graphs here is an example of how to implement the algorithm iteratively:
import networkx as nx
G = nx.DiGraph()
G.add_nodes_from([1,2,3])
G.add_edges_from([(2, 1), (3, 1), (2, 3)])
G.node[1]['weight'] = 1
G.node[2]['weight'] = 2
G.node[3]['weight'] = 3
def activate_node(g, start_node):
stack = [start_node]
ws = []
while stack:
node = stack.pop()
preds = g.predecessors(node)
stack += preds
print('%s -> %s' % (node, preds))
for pred in preds:
ws.append(g.node[pred]['weight'])
print('weights: %r' % ws)
return sum(ws)
print('total sum %d' % activate_node(G, 1))
this code prints:
1 -> [2, 3]
3 -> [2]
2 -> []
2 -> []
weights: [2, 3, 2]
total sum 7
Note
you can reverse the direction of the directed graph using DiGraph.reverse()
if you need to use DFS or something else you can reverse the graph to get the predecessor as just the directly connected neighbours of that node. Using this, algorithms like DFS might be easier to use.
I am trying to simulate a random traversal through a directed networkx graph. The pseudo code is as follows
Create graph G with nodes holding the value true or false.
// true -> visited, false -> not visited
pick random node N from G
save N.successors as templist
while true
nooptions = false
pick random node N from templist
while N from templist has been visited
remove N from templist
pick random node N from templist
if templist is empty
nooptions = true
break
if nooptions = true
break
save N.successors as templist
Is there are a more efficient way of marking a path as traveled other than
creating a temporary list and removing the elements if they are marked as visited?
EDIT
The goal of the algorithm is to pick a node at random in the graph. Pick a random successor/child of that node. If it is unvisited, go there and mark it as visited. Repeat until there are either no successors/children or there are no unvisited successors/children
Depending on the size of your graph, you could use the built-in all_pairs_shortest_path function. Your function would then be basically:
G = nx.DiGraph()
<add some stuff to G>
# Get a random path from the graph
all_paths = nx.all_pairs_shortest_path(G)
# Choose a random source
source = random.choice(all_paths.keys())
# Choose a random target that source can access
target = random.choice(all_paths[source].keys())
# Random path is at
random_path = all_paths[source][target]
There doesn't appear to be a way to just generate the random paths starting at source that I saw, but the python code is accessible, and adding that feature would be straightforward I think.
Two other possibilities, which might be faster but a little more complicated/manual, would be to use bfs_successors, which does a breadth-first search, and should only include any target node once in the list. Not 100% sure on the format, so it might not be convenient.
You could also generate bfs_tree, which generates a subgraph with no cycles to all nodes that it can reach. That might actually be simpler, and probably shorter?
# Get random source from G.node
source = random.choice(G.node)
min_tree = nx.bfs_tree(G, source)
# Accessible nodes are any node in this list, except I need to remove source.
all_accessible = min_tree.node.keys()
all_accessible.remove(source)
target = random.choice(all_accessible.node.keys())
random_path = nx.shortest_path(G, source, target)
I'm working on some code for a directed graph in NetworkX, and have hit a block that's likely the result of my questionable programming experience. What I'm trying to do is the following:
I have a directed graph G, with two "parent nodes" at the top, from which all other nodes flow. When graphing this network, I'd like to graph every node that is a descendant of "Parent 1" one color, and all the other nodes another color. Which means I need a list Parent 1's successors.
Right now, I can get the first layer of them easily using:
descend= G.successors(parent1)
The problem is this only gives me the first generation of successors. Preferably, I want the successors of successors, the successors of the successors of the successors, etc. Arbitrarily, because it would be extremely useful to be able to run the analysis and make the graph without having to know exactly how many generations are in it.
Any idea how to approach this?
You don't need a list of descendents, you just want to color them. For that you just have to pick a algorithm that traverses the graph and use it to color the edges.
For example, you can do
from networkx.algorithms.traversal.depth_first_search import dfs_edges
G = DiGraph( ... )
for edge in dfs_edges(G, parent1):
color(edge)
See https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.traversal.depth_first_search.dfs_edges.html?highlight=traversal
If you want to get all the successor nodes, without passing through edges, another way could be:
import networkx as nx
G = DiGraph( ... )
successors = nx.nodes(nx.dfs_tree(G, your_node))
I noticed that if you call instead:
successors = list(nx.dfs_successors(G, your_node)
the nodes of the bottom level are somehow not included.
Well, the successor of successor is just the successor of the descendants right?
# First successors
descend = G.successors(parent1)
# 2nd level successors
def allDescendants(d1):
d2 = []
for d in d1:
d2 += G.successors(d)
return d2
descend2 = allDescendants(descend)
To get level 3 descendants, call allDescendants(d2) etc.
Edit:
Issue 1:
allDescend = descend + descend2 gives you the two sets combined, do the same for further levels of descendants.
Issue2: If you have loops in your graph, then you need to first modify the code to test if you've visited that descendant before, e.g:
def allDescendants(d1, exclude):
d2 = []
for d in d1:
d2 += filter(lambda s: s not in exclude, G.successors(d))
return d2
This way, you pass allDescend as the second argument to the above function so it's not included in future descendants. You keep doing this until allDescandants() returns an empty array in which case you know you've explored the entire graph, and you stop.
Since this is starting to look like homework, I'll let you figure out how to piece all this together on your own. ;)
So that the answer is somewhat cleaner and easier to find for future folks who stumble upon it, here's the code I ended up using:
G = DiGraph() # Creates an empty directed graph G
infile = open(sys.argv[1])
for edge in infile:
edge1, edge2 = edge.split() #Splits data on the space
node1 = int(edge1) #Creates integer version of the node names
node2 = int(edge2)
G.add_edge(node1,node2) #Adds an edge between two nodes
parent1=int(sys.argv[2])
parent2=int(sys.argv[3])
data_successors = dfs_successors(G,parent1)
successor_list = data_successors.values()
allsuccessors = [item for sublist in successor_list for item in sublist]
pos = graphviz_layout(G,prog='dot')
plt.figure(dpi=300)
draw_networkx_nodes(G,pos,node_color="LightCoral")
draw_networkx_nodes(G,pos,nodelist=allsuccessors, node_color="SkyBlue")
draw_networkx_edges(G,pos,arrows=False)
draw_networkx_labels(G,pos,font_size=6,font_family='sans-serif',labels=labels)
I believe Networkx has changed since #Jochen Ritzel 's answer a few years ago.
Now the following holds, only changing the import statement.
import networkx
from networkx import dfs_edges
G = DiGraph( ... )
for edge in dfs_edges(G, parent1):
color(edge)
Oneliner:
descendents = sum(nx.dfs_successors(G, parent).values(), [])
nx.descendants(G, parent)
more details: https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.dag.descendants.html