Tag Archives: networkx

Beautiful Networks

I’ve had a secret project running in the background this week two weeks ago (how time flies!), a continuation of my work on bias reduction for traceroute sampling. It would be nice if this had applications to global health, but unfortunately (and uncharacteristically) I can’t think of any. It is a great opportunity for visualizing networks, though, a topic worthy of a quick post.

The bowl-of-spaghetti network visualization has been a staple of complex networks research for the last decade. I’m not convinced that there is anything interesting to learn from real world networks by drawing them in 2 or 3 dimensions, but the graphics a seriously eye catching. And I’m not convinced that there isn’t anything to learn from them, either. I invite you to convince me in the comments.


What my side project has reminded me of, however, is the value of drawing networks in 2 dimensions for illustrating the principles of network algorithms and network statistics. And if the topic of study is complex or real-world or random networks, than a little bit of spaghetti in the graphic seems appropriate.

There are a lot of nice tools for doing this now, and just collecting the things I should consider in one place makes this post worthwhile for me. I learn towards a Pythonic solution of networkx driving graphviz, but there are some javascript options out there now that seem promising (jit, protovis, possibly more from a stackoverflow question) in. And for those looking for a less command-line-based solution, the Pajek system seems like a good route.

As for what to graph, here are my thoughts. The Erdos-Renyi graph doesn’t look good, and the Preferential Attachment graph doesn’t look good. Use them for your theorems and for your simulations, but when it comes time to draw something, consider a random geometric graph. And since these can be a little dense, you might want an “edge-percolated random geometric graph”.

I did have a little trouble with this approach, too, when I was drawing minimum spanning trees, because the random geometric points end up being placed really close together occasionally. So maybe the absolutely best random graph for illustrations would be a geometric graph with vertices from a “hard core” model, which is to say random conditioned on being a minimum distance apart. Unfortunately, it is an open question how to efficiently generate hard-core points. But it’s not hard to fake:

More informative?

Want some of your own? Here’s the code.

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Filed under probability

ACO in Python: Shortest Paths in NetworkX

I’m supposed to be doing the final edits on the journal version of this old paper of mine (jointly with Greg Sorkin and David Gamarnik), but I’ve thought of a way to procrastinate.

Instead of checking the proofs that the length of the shortest path in my weigthed width-2 strip is \frac{p^2(1+p)^2}{(3p^2+1)} n, I’ll make a quick blog post about verifying this claim numerically (in python with networkx). This also gives me a chance to try out the new networkx, which is currently version 1.0rc1. I think it has changed a bit since we last met.

from pylab import *
from networkx import *

G = Graph()
for u, v in grid_2d_graph(100, 2).edges():
    G.add_edge(u, v, weight=rand() < .5)

wt, p = bidirectional_dijkstra(G, (0,0), (99,1))

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Filed under combinatorial optimization

Dense-Subset Break-the-Bank Challenge

I’m preparing for my first global travel for global health, but the net is paying attention to a paper that I think I’ll like, and I want to mention it briefly before I fly.

Computational Complexity and Information Asymmetry in Financial Products is 27 pages of serious TCS, but it is so obviously applicable that people outside of our particular ivory tower, and even outside of academia entirely are blogging and twittering about it, and even reading it!

Freedom to Tinker has a nice summary of this paper, if you want to know what it’s about in a hurry.

Mike Trick makes the salient observation that NP-hard doesn’t mean computers can’t do it. But the assumption that this paper is based on is not about worst-case complexity; it is, as it should be, based on an assumption about the average-case complexity of a particular optimization problem over a particular distribution.

As it turns out, this is an average-case combinatorial optimization problem that I know and love, the densest subgraph problem. My plan is to repeat the problem here, and share some Python code for generating instances of it. Then, you, me, and everyone, can have a handy instance to try optimizing. I think that this problem is pretty hard, on average, but there is a lot more chance of making progress on an algorithm for it than for cracking the P versus NP nut. Continue reading


Filed under combinatorial optimization, cryptography, TCS

August is Too-Many-Projects Month

(Tap… tap… tap… is this thing on? Good.)

July was vacation month, where I went on a glorious bike tour of the Oregon/California coast, and learned definitively that I don’t like biking on the side of a highway all day. Don’t worry, I escaped in Coos Bay and took trains and buses between Eugene, Santa Cruz, Berkeley, and SF for a vacation more my speed.

But now that I’m back, August is turning out to be project month. I have 3 great TCS applications to global health in the pipeline, and I have big plans to tell you about them soon. But one mixed blessing about these applications is that people actually want to see the results, like, yesterday! So first I have to deal with the results, and then I can write papers and blogs about the techniques.

Since Project Month is a little over-booked with projects, I’m going to have to triage one today. You’ve heard of the NetFlix Challenge, right? Well, github.com is running a smaller scale recommendation contest, and I was messing around with personal page rank, which seems like a fine approach for recommending code repositories to hackers. I haven’t got it working very well (best results, 15% of holdout set recovered), but I was having fun with it. Maybe someone else will take it up, let me know if you get it to work; networkx + data = good times.

    f = open('download/data.txt')
    for l in f:
        u_id, r_id = l.strip().split(':')
        G.add_edge(user(u_id), repo(r_id))

[get the code]


Filed under combinatorial optimization, software engineering, TCS

MCMC: Running a chain, making it look easy

As I was saying in my last post, I’ve been getting interested in actually running Markov Chain Monte Carlo algorithms, instead of trying to prove things about their asymptotic performance. It seems like the “stats” way to do this is to use R and WinBUGS, but I’ve always thought that R programming looks messy. Python is easier on my eyes.

So, it’s my good fortune that PyMC exists. This means I don’t need to do any hard work, like coding a Gibbs sampler or learning R. Let me show you.

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Filed under MCMC