Dear Tiago,
I have a directed graph of about half a million nodes and approximately a
million edges following scale free behaviour and a power law degree
distribution. To test some of my hypothesis, I would like to generate random
smaller graphs (about 50 up to 200 nodes) representative of the big one.
When I used a sample function that samples straight away from the real
distribution of the big network, I have following problems:
- I generate unconnected nodes with both 0 in AND out degree.
- I generate small sub parts of a few nodes that are not connected to the
main graph.
- If only sampling from nodes with at least 1 degree, the generated graph is
coherent, but not representative anymore as I need a big portion of nodes
with either only one in or one out degree.
Here is the part of my script I used for that, where samples are drawn from
dictionaries of the degrees:
def sample_in():
a=np.random.randint(num)
k_in = in_degrees[a]
return k_in
def sample_out():
if sample_in()==0:
b=np.random.randint(num_out)
k_out=out_zero_zeros.values()[b]
return k_out
else:
b=np.random.randint(num)
k_out=out_degrees[b]
return k_out
N=200
g=gt.random_graph(N, lambda:(sample_in(), sample_out()),
model="constrained-configuration", directed=True)
I also tried sampling from a list of tuples as you have mentioned before in
the forum, but I didn't receive any results, as the tuples randomly drawn
from my list might not be combinable.
degs=[(7,1),(4,3),(5,6),(2,4),(6,8),(2,0),(3,5),(0,3),(2,7),(2,1)]
g = gt.random_graph(4, lambda i: degs[i], directed=True)
- Is there any option I could active that would help me in those cases I
described above?
- Is there a better way how to create representative small networks?
Any help on that issue will be much appreciated.
Best wishes,
Jana
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I am curious what is being used to calculate the standard deviation of the
average in gt.vertex_average and gt.edge_average
>>> t2=gt.Graph()
>>> t2.add_vertex(2)
>>> t2.add_edge(t2.vertex(0), t2.vertex(1))
>>> gt.vertex_average(t2, "in")
(0.5, 0.35355339059327373)
Now, shouldn't std be σ(n)=sqrt(((0-0.5)^2+(1-0.5)^2)/2)=0.5 ?
also q(n-1)=sqrt((0.5^2+0.5^2)/(2-1))~=0.70710
0.3535 is sqrt(2)/4 which happens to be σ(n-1)/2, so it seems there is some
relation to that.
A little bigger graph.
>>> t3=gt.Graph()
>>> t3.add_vertex(5)
>>> t3.add_edge(t3.vertex(0), t3.vertex(1))
>>> gt.vertex_average(t3, "in")
(0.2, 0.17888543819998318)
Now, we should have 0,1,0,0,0 series for vertex incoming degree.
So Windows calc gives σ(n)=0.4 and σ(n-1)~=0.44721, so where does 0.1788854
come from ?
Reason, I am asking because, I have a large graph, where the average looks
quite alright but the std makes no sense, as going by the histogram, degree
values are quite a bit more distributed than the std would indicate.
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Dear Graph-Tool Community,
I am interested in analysing the hierarchical partitions generated by the nested blockmodel. Specifically, after I have generated a nested SBM; I would then like to post-process this and calculate measures such as eigenvector centrality for a given hierarchical node; save this as a property, and then in visualisation apply either a size or colormap constraint to said node weighted by its centrality.
Using the collection data;
g = gt.collection.data["celegansneural”]
state = gt.minimize_nested_blockmodel_dl(g)
I can then ascertain what my levels are with;
l1state = state.levels[1].g
l2state = state.levels[2].g
etc.
I can then calculate eigenvector centrality of a given hierarchical partition as follows;
ee1, x1 = gt.eigenvector(l1state)
ee2, x2 = gt.eigenvector(l2state)
1) This presumably then needs to be saved as a hvprops(?!). But, I am unclear how to do this, not least in a way that I know for sure that the correct hierarchical vertices within l1state and l2state are aligning to the generated centrality measures of x1 and x2, respectively.
2) Furthermore, if/when that is achieved, how can I call upon this in drawing, for example to size the level 1 hierarchical vertices according to centrality, or level 2 vertices by another measure, etc.?
Hugely grateful for any solutions!
James

Dear community / Tiago
I have a hierarchical partition of a nested block state.
The original network contained 4453 vertices and 50051 edges.
state.print_summary()
l: 0, N: 4453, B: 126
l: 1, N: 126, B: 46
l: 2, N: 46, B: 20
l: 3, N: 20, B: 9
l: 4, N: 9, B: 3
l: 5, N: 3, B: 1
I want to extract the community label of each vertex of each possible hierarchical level.
To do this I wrote a loop based upon the guide at https://graph-tool.skewed.de/static/doc/demos/inference/inference.html
Where vertexblocksdf is simply a df populated with the vertex numbers 0-4452.
for idx in range(len(vertexblocksdf)):
r = levels[0].get_blocks()[idx] # group membership of node idx in level 0
vertexblocksdf.ix[idx, 'level0'] = r
r = levels[0].get_blocks()[r] # group membership of node idx in level 1
vertexblocksdf.ix[idx, 'level1'] = r
r = levels[0].get_blocks()[r] # group membership of node idx in level 2
vertexblocksdf.ix[idx, 'level2'] = r
r = levels[0].get_blocks()[r] # group membership of node idx in level 3
vertexblocksdf.ix[idx, 'level3'] = r
r = levels[0].get_blocks()[r] # group membership of node idx in level 4
vertexblocksdf.ix[idx, 'level4'] = r
r = levels[0].get_blocks()[r] # group membership of node idx in level 5
vertexblocksdf.ix[idx, 'level5'] = r
But, I am getting strange results. My level0 column variables make sense, with 126 possibilities (as per l0 above). But my level1 column is a number between 0 and 13; of which none of my levels have 14 blocks. My level2 output is either 0 or 1, again doesn’t make sense! Level3-5 are all simply 0.
*this also reproduces the same behaviour if done manually without loop.
Any ideas??
James

Hi,
I was wondering if there is any way to assign vertex properties while
adding edges to the graph. for example using "add_edge_list" I can assign
edge properties but later I have to iterate through all vertices again to
assign their properties.
I know this is not a problem when the vertex property is of the type "int"
or "float" because then one can use "vprop.a = values", but in case of
"string" and "object" this method doesn't work
What would be the best/fastest way to handle this situation.
I guess it would be very helpful to extend the "add_edge_list" function to
accept vertex property in some way.
cheers,
--
Mohsen

Dear Tiago,
Thanks for building this wonderful package!
As a novice in Python I'm struggling to install this package- My operating
system is MacOS and I installed graph-tool via Homebrew.
It seems the installation was successful. When compiling, the command
'./configure' doesn't work, could you please give the further instructions?
Many thanks,
Yingjie
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I ran mcmc_equilibrate on a nested block state model in a weighted graph. As
per instructions, I copied the initially computed state in another object
with increased hierarchy depth to 10. However, this fixed the depth to 10.
Everything computed afterwards has depth 10 even if is clear that after 3 or
4 levels the nodes converge to one.
There are many empty branches and when I try to plot it with empty_branches
= False, I get an error stating it is not a tree.
RuntimeError: Invalid hierarchical tree: No path from source to target.
Did anybody perform any similar analyses?
The hierarchy after mcmc_equilibrate:
<NestedBlockState object, with base <BlockState object with 24 blocks (24
nonempty), degree-corrected, with 1 edge covariate, for graph <Graph
object, undirected, with 230 vertices and 11230 edges, edges filtered by
(<PropertyMap object with key type 'Edge' and value type 'bool', for
Graph 0x7fc3a89f1210, at 0x7fc3a64911d0>, False), vertices filtered by
(<PropertyMap object with key type 'Vertex' and value type 'bool', for Graph
0x7fc3a89f1210, at 0x7fc3a64912d0>, False) at 0x7fc3a89f1210>, at
0x7fc3a6491950>, and 10 levels of sizes [(230, 24), (24, 5), (5, 1), (1, 1),
(1, 1), (1, 1), (1, 1), (1, 1), (1, 1), (1, 1)] at 0x7fc3a6491590>
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Hi,
I'm using graph-tool to try to generate random graphs with a sequence of
degrees. For example, in a 3-node graph, I generated a random graph with
all nodes with input degrees 1 and output degrees 1.
My code:
>>> import graph_tool.all as gt>>> def deg_sampler():... return 1,1... >>> g = gt.random_graph(3,deg_sampler,parallel_edges=True, self_loops=False)>>> gt.graph_draw(g)
Can I generate a random graph defining the input and output degrees of each
node? For example, tree nodes with respectively the input degrees (1, 2, 0)
and output degrees (1, 0, 2).
Thanks,
Alvaro

Hi,
I have a rather silly question but I hope it will not hinder anyone from
answering.
I have been having difficulties finding publications which use graph-tool
and apply it for researching a network (not for comparison with other
methods or for developing their own method). Does anyone have any link to
such applications?
I am interested in how people discuss/observe network properties or validate
their observation of hierarchical block models.
Thanks!
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