Develop Reference

Find all shortest paths between all pairs of nodes in NetworkX

I am trying to get all shortest paths between all pairs of nodes in an undirected unweighted graph. I am currently using nx.all_pairs_shortest_path(), but I don't understand why it only returns one shortest path for every pair of nodes. There are cycles in my graph so there should exist multiple shortest paths between certain nodes. Any suggestions?

Iterate over all nodes in the graph:
results = []
for n1 in G.nodes():
for n2 in G.nodes():
shortest_path = nx.single_source_dijkstra(G, source=n1, target=n2, weight=f)
results.append(shortest_path)

I may be late, but I just came across the same problem and this was my solution:
def all_shortest_paths(G):
a = list(nx.all_pairs_shortest_path(G))
all_sp_list = []
for n in range(len(G.nodes)):
a1 = a[n][1]
for k,v in a1.items():
all_sp_list.append(len(v))
return all_sp_list
Every other way I tried was getting very very slow because my graph had a bunch of nodes, so this was my fastest solution.

I stumbled upon this problem myself and arrived her in my quest for a solution. unfortunately networkx doesn't have a function to calculate all the shortest pathes for every pair of node. Moreover the answer from Igor Michetti wasn't giving what i wanted at all but it might have been tweekable.
The answer from math_noob was good because it was close enough for me to make up a solution but the problem was that it was way way too slow.
def single_source_shortest_paths(graph,source):
shortest_paths_dict = {}
for node in graph:
shortest_paths_dict[node] = list(nx.all_shortest_paths(graph,source,node))
return shortest_paths_dict
def all_shortest_paths(graph):
for source in graph:
yield source, single_source_shortest_paths(source)
So i went back on networkx documentation and try to find one last time if there was any function i could use. but there was none so i decided i would implment it myself.So i first tried to implement everything by had which was a bit chaotic to only realise that it was a bit better but not that much so i decided i would try to look into the source code and found there a holy grail which is the nx.predecessor function.
This function is called on the graph and the source node only so it doesn't depends on the target node and it is the one doing most of the hard work. So i just recreated the function single_source_shortest_paths but by calling only once nx.predecessor per source node and then doing the same as all_shortest_path which only consist of calling another function with the right arguments.
def single_source_shortest_paths_pred(graph,source):
shortest_paths_dict = {}
pred = nx.predecessor(graph,source)
for node in graph:
shortest_paths_dict[node] = list(nx.algorithms.shortest_paths.generic._build_paths_from_predecessors([source], node, pred))
return shortest_paths_dict
In terms of time nx.predecessor takes the majority of the time to execute so the second function is around n times faster where n is the number of nodes in the graph

Is there a way to detect changes in a graph created with NetworkX?

I am a beginner Python programmer, and I would really appreciate your help with the following issue.
I have a first script that creates a graph and saves it as a Pickle file:
import networkx as nx
G = nx.Graph()
#Some code lines to add nodes and edges...
nx.write_gpickle(G, "graph_file.gpickle")
Then, I have a second script where I want to read the Pickle file and detect any changes in the graph nodes attributes, in case the first script was rerun with different values for the nodes attributes:
import networkx as nx
G = nx.read_gpickle("graph_file.gpickle")
#I need to implement something like this:
for node in G.nodes():
if node["attribute"] changed from previous value:
print(f"The attribute of the node {node} changed from {previous value of node["attribute"]} to {new value of node["attribute"]}")

maya python, polyvertexpernormal

So in a nutshell I am needing to export the vertex normals from a character into a text file, or whatever, and then reimport them onto the same character in a different scene.
I have the import export part working in a method that I think is ok, but actually going through the loop and setting the normal on each vertex is taking over twenty minutes and usually overloads the ram on my machine and crashes maya.
I guess I am looking for a way to make my code more efficient or just run faster, any advice would be appreciated. Thanks.
def ImoNorms(self):
ll = mc.ls ('head.vtxFace[*][*]')
input = open('My desktop.txt', 'r')
spltOne = ll[:len(ll)/2]
spltTwo = ll[len(ll)/2:]
i = 0
for each in spltOne:
CurrentLine = input.readline()
kk = re.split(r'\[|\]|\,|\/n|\ ',CurrentLine)
aa = float(kk[1])
aa = round(aa, 3)
bb = float(kk[3])
bb = round(bb,3)
cc = float(kk[5])
cc = round(cc,3)
mc.select(each)
mc.polyNormalPerVertex(xyz =(aa, bb, cc))
i = i + 1
if i%1000 == 0:
print i
init()
Sorry for the formatting issues, still new to this site.

+1 to using OpenMaya if you want better performance.
Check out MFnMesh.getNormals and MFnMesh.setNormals. I admit I haven't used these methods myself, but if it's anything like MFnMesh.setPoints it should be a significant boost in speed as it's setting the normals all at once. Seems like you don't have to deal with its history either.
Here's an example on its usage that will re-direct all of a sphere's vert normals to point down. (Go to Display->Polygons->Vertex Normals to visualize the normals)
import maya.OpenMaya as OpenMaya
# Create a sphere to change vert normals with
mesh_obj, _ = cmds.polySphere()
# Wrap sphere as MDagPath object
sel = OpenMaya.MSelectionList()
sel.add(mesh_obj)
dag_path = OpenMaya.MDagPath()
sel.getDagPath(0, dag_path)
# Pass sphere to mesh function set
mesh_fn = OpenMaya.MFnMesh(dag_path)
# Create empty vector array
vec_array = OpenMaya.MFloatVectorArray()
# Get sphere normals and stuff data in our vector array
mesh_fn.getNormals(vec_array, OpenMaya.MSpace.kObject)
for i in range( vec_array.length() ):
# Point all normals downwards
vec_array[i].assign( OpenMaya.MFloatVector(0, -1, 0) )
# Apply normals back to sphere
mesh_fn.setNormals(vec_array, OpenMaya.MSpace.kObject)
You may also want to consider a different way on how you read your file instead of reading each line one by one. Maybe using json.dumps to store the data to a file and json.loads to retrieve the data. This could potentially speed things up.

What you have will be very slow because you are creating a lot of history on your mesh: if you exit out of the loop after a couple of iterations you'll see that your mesh is accumulating a polyNormalPerVertex node for every iteration.
Unfortunately there's no way to turn of construction history for this command (which seems like an oversight: most commands have a ch flag for exactly this purpose). So the first thing to try is to add an mc.delete(ch=True) after every polyNormalPerVertex call. That will be much faster and it might be enough for what you're doing.
Otherwise you'll need to use the OpenMaya api, which is a bit harder than cmds but will let you do bulk normal operations faster. I would get the cmds version working first and see if it's good enough, it should be much more performant without the history overhead.
UPDATE
Unless you want to learn the API to do this, the right thing is probably:
Save out the mesh with the right normals as an MB or MA file
in the other file, load that mesh and use Transfer Attributes to copy the normals across.
Delete history and remove the mesh you loaded in (2)
That gets you off the hook for both making your own file format and for perf issues, plus it gives you pre-made options for cases where the topology does not line up for some reason

Creating publication-quality geometric figures in Python

I am a mathematician. Recently, I became the editor of the puzzles and problems column for a well-known magazine. Occasionally, I need to create a figure to accompany a problem or solution. These figures mostly relate to 2D (occasionally, 3D) euclidean geometry (lines, polygons, circles, plus the occasional ellipse or other conic section). The goal is obtaining figures of very high quality (press-ready), with Computer Modern ("TeX") textual labels. My hope is finding (or perhaps helping write!) a relatively high-level Python library that "knows" euclidean geometry in the sense that natural operations (e.g., drawing a perpendicular line to a given one passing through a given point, bisecting a given angle, or reflecting a figure A on a line L to obtain a new figure A') are already defined in the library. Of course, the ability to create figures after their elements are defined is a crucial goal (e.g., as Encapsulated Postscript).
I know multiple sub-optimal solutions to this problem (some partial), but I don't know of any that is both simple and flexible. Let me explain:
Asymptote (similar to/based on Metapost) allows creating extremely high-quality figures of great complexity, but knows almost nothing about geometric constructions (it is a rather low-level language) and thus any nontrivial construction requires quite a long script.
TikZ with package tkz-euclide is high-level, flexible and also generates quality figures, but its syntax is so heavy that I just cry for Python's simplicity in comparison. (Some programs actually export to TikZ---see below.)
Dynamic Geometry programs, of which I'm most familiar with Geogebra, often have figure-exporting features (EPS, TikZ, etc.), but are meant to be used interactively. Sometimes, what one needs is a figure based on hard specs (e.g., exact side lengths)---defining objects in a script is ultimately more flexible (if correspondingly less convenient).
Two programs, Eukleides and GCLC, are closest to what I'm looking for: They generate figures (EPS format; GCLC also exports to TikZ). Eukleides has the prettiest, simplest syntax of all the options (see the examples), but it happens to be written in C (with source available, though I'm not sure about the license), rather limited/non-customizable, and no longer maintained. GCLC is still maintained but it is closed-source, its syntax is significantly worse than Eukleides's, and has certain other unnatural quirks. Besides, it is not available for Mac OS (my laptop is a Mac).
Python has:
Matplotlib, which produces extremely high-quality figures (particularly of functions or numerical data), but does not seem to know about geometric constructions, and
Sympy has a geometry module which does know about geometric objects and constructions, all accessible in delightful Python syntax, but seems to have no figure-exporting (or even displaying?) capabilities.
Finally, a question: Is there a library, something like "Figures for Sympy/geometry", that uses Python syntax to describe geometric objects and constructions, allowing to generate high-quality figures (primarily for printing, say EPS)?
If a library with such functionality does not exist, I would consider helping to write one (perhaps an extension to Sympy?). I will appreciate pointers.

There is a way to generate vector images with matplotlob, outputting with the library io to a vector image (SVG) with this approach.
I personally tried to run the code of the approach (generate a vectorial histogram) in that webpage as a python file, and it worked.
The code:
import numpy as np
import matplotlib.pyplot as plt
import xml.etree.ElementTree as ET
from io import BytesIO
import json
plt.rcParams['svg.fonttype'] = 'none'
# Apparently, this `register_namespace` method is necessary to avoid garbling
# the XML namespace with ns0.
ET.register_namespace("", "http://www.w3.org/2000/svg")
# Fixing random state for reproducibility
np.random.seed(19680801)
# --- Create histogram, legend and title ---
plt.figure()
r = np.random.randn(100)
r1 = r + 1
labels = ['Rabbits', 'Frogs']
H = plt.hist([r, r1], label=labels)
containers = H[-1]
leg = plt.legend(frameon=False)
plt.title("From a web browser, click on the legend\n"
"marker to toggle the corresponding histogram.")
# --- Add ids to the svg objects we'll modify
hist_patches = {}
for ic, c in enumerate(containers):
hist_patches['hist_%d' % ic] = []
for il, element in enumerate(c):
element.set_gid('hist_%d_patch_%d' % (ic, il))
hist_patches['hist_%d' % ic].append('hist_%d_patch_%d' % (ic, il))
# Set ids for the legend patches
for i, t in enumerate(leg.get_patches()):
t.set_gid('leg_patch_%d' % i)
# Set ids for the text patches
for i, t in enumerate(leg.get_texts()):
t.set_gid('leg_text_%d' % i)
# Save SVG in a fake file object.
f = BytesIO()
plt.savefig(f, format="svg")
# Create XML tree from the SVG file.
tree, xmlid = ET.XMLID(f.getvalue())
# --- Add interactivity ---
# Add attributes to the patch objects.
for i, t in enumerate(leg.get_patches()):
el = xmlid['leg_patch_%d' % i]
el.set('cursor', 'pointer')
el.set('onclick', "toggle_hist(this)")
# Add attributes to the text objects.
for i, t in enumerate(leg.get_texts()):
el = xmlid['leg_text_%d' % i]
el.set('cursor', 'pointer')
el.set('onclick', "toggle_hist(this)")
# Create script defining the function `toggle_hist`.
# We create a global variable `container` that stores the patches id
# belonging to each histogram. Then a function "toggle_element" sets the
# visibility attribute of all patches of each histogram and the opacity
# of the marker itself.
script = """
<script type="text/ecmascript">
<![CDATA[
var container = %s
function toggle(oid, attribute, values) {
/* Toggle the style attribute of an object between two values.
Parameters
----------
oid : str
Object identifier.
attribute : str
Name of style attribute.
values : [on state, off state]
The two values that are switched between.
*/
var obj = document.getElementById(oid);
var a = obj.style[attribute];
a = (a == values[0] || a == "") ? values[1] : values[0];
obj.style[attribute] = a;
}
function toggle_hist(obj) {
var num = obj.id.slice(-1);
toggle('leg_patch_' + num, 'opacity', [1, 0.3]);
toggle('leg_text_' + num, 'opacity', [1, 0.5]);
var names = container['hist_'+num]
for (var i=0; i < names.length; i++) {
toggle(names[i], 'opacity', [1, 0])
};
}
]]>
</script>
""" % json.dumps(hist_patches)
# Add a transition effect
css = tree.getchildren()[0][0]
css.text = css.text + "g {-webkit-transition:opacity 0.4s ease-out;" + \
"-moz-transition:opacity 0.4s ease-out;}"
# Insert the script and save to file.
tree.insert(0, ET.XML(script))
ET.ElementTree(tree).write("svg_histogram.svg")
Previously, you need to pip install the required libraries on the top lines, and it successfully saved a SVG file with a plot (you can read the file and zoomwant in the histogram and you will get no pixels, as the image is generated with mathematicals functions).
It (obviously for our time) uses python 3.
You then could import the SVG image within your TeX document for the publication rendering.
I hope it may help.
Greetings,
Javier.

Determining Betweenness Centrality With The Igraph Library

I am a very, very mediocre programmer, but I still aim to use the igraph python library to determine the effect of a user's centrality in a given forum to predict his later contributions to that forum.
I got in touch with someone else who used the NetworkX library to do something similar, but given the current size of the forum, calculating exact centrality indices is virtually impossible--it just takes too much time.
This was his code though:
import networkx as netx
import sys, csv
if len(sys.argv) is not 2:
print 'Please specify an input graph.'
sys.exit(1)
ingraph = sys.argv[1]
graph = netx.readwrite.gpickle.read_gpickle(ingraph)
num_nodes = len(graph.nodes())
print '%s nodes found in input graph.' % num_nodes
print 'Recording data in centrality.csv'
# Calculate all of the betweenness measures
betweenness = netx.algorithms.centrality.betweenness_centrality(graph)
print 'Betweenness computations complete.'
closeness = netx.algorithms.centrality.closeness_centrality(graph)
print 'Closeness computations complete.'
outcsv = csv.writer(open('centrality.csv', 'wb'))
for node in graph.nodes():
outcsv.writerow([node, betweenness[node], closeness[node]])
print 'Complete!'
I tried to write something similar with the igraph library (which allows to make quick estimates rather than exact calculations), but I cannot seem to write data to a CSV file.
My code:
import igraph
import sys, csv
from igraph import *
graph = Graph.Read_Pajek("C:\karate.net")
print igraph.summary(graph)
estimate = graph.betweenness(vertices=None, directed=True, cutoff=2)
print 'Betweenness computation complete.'
outcsv = csv.writer(open('estimate.csv', 'wb'))
for v in graph.vs():
outcsv.writerow([v, estimate[vs]])
print 'Complete!'
I can't find how to call individual vertices (or nodes, in NetworkX jargon) in the igraph documentation, so that's where I am getting error messages). Perhaps I am forgetting something else as well; I am probably too bad a programmer to notice :P
What am I doing wrong?

So, for the sake of clarity, the following eventually proved to do the trick:
import igraph
import sys, csv
from igraph import *
from itertools import izip
graph = Graph.Read_GML("C:\stack.gml")
print igraph.summary(graph)
my_id_to_igraph_id = dict((v, k) for k, v in enumerate(graph.vs["id"]))
estimate = graph.betweenness(directed=True, cutoff=16)
print 'Betweenness computation complete.'
print graph.vertex_attributes()
outcsv = csv.writer(open('estimate17.csv', 'wb'))
outcsv.writerows(izip(graph.vs["id"], estimate))
print 'Complete!'

As you already noticed, individual vertices in igraph are accessed using the vs attribute of your graph object. vs behaves like a list, so iterating over it will yield the vertices of the graph. Each vertex is represented by an instance of the Vertex class, and the index of the vertex is given by its index attribute. (Note that igraph uses continuous numeric indices for both the vertices and the edges, so that's why you need the index attribute and cannot use your original vertex names directly).
I presume that what you need is the name of the vertex that was stored originally in your input file. Names are stored in the name or id vertex attribute (depending on your input format), so what you need is probably this:
for v in graph.vs:
outcsv.writerow([v["name"], estimate[v.index]])
Note that vertex attributes are accessed by indexing the vertex object as if it was a dictionary. An alternative is to use the vs object directly as a dictionary; this will give you a list containing the values of the given vertex attribute for all vertices. E.g.:
from itertools import izip
for name, est in izip(graph.vs["name"], estimate):
outcsv.writerow([name, est])
An even faster version using generator expressions:
outcsv.writerows(izip(graph.vs["name"], estimate))