Visual Exploration of Complex Networks

jweebo writes "Seed magazine has a story on complexity, and how it can be visually represented with fascinating results. From the article: 'Complexity is everywhere. It's a structural and organizational principle that reaches almost every field imaginable, from genetics and social networks to food webs and stock markets ...Collected here are a few of the many intriguing, and often beautiful, images that illustrate how the whole is more than the sum of its parts.'"

Comments

Wow

[Eightyford]

Wow, a winamp visualization.

Let me just say...

[The Living Fractal]

I have a book, about a thousand pages long, by a certain author of a certain mathematics program (who I will not name here) that basically says the same thing.

Translation for the 1000+ pages:

"omGz)R patterns pwnz joO!"

Really though, the guy goes on and on about his 'new kind of science' and after a thousand pages gets pretty much nowhere.

But hey, it was complex, man! Serious!

TLF

Let me guess...

[jd]

You've been reading "Fractal Geometry of Nature" by Benoit Mandelbrot. Very nice illustrations and the section on how fractals all started and another on fractal dimensions were good, but otherwise the book was far too vague and had few proofs. This demonstrates Heisenberg's Writing Principle, which states that you can either know bout a topic or write about it, but not at the same time.

Re:Let me guess...

[jthayden]

Heisenberg's Writing Principle, which states that you can either know bout a topic or write about it, but not at the same time.

Where does this leave reading about a topic?

Information Architecture & Prefuse

[Lord Satri]

The article is a little short, I would have liked more more more!! :-)

May I suggest Information Architecture from Peter Morville. He is also co-founder and president of the Information Architecture Institute.

May I also suggest taking a look at Prefuse, an open source project to interactively vizualize organized information (still in beta however).

Re:Information Architecture & Prefuse

[thrillseeker]

The article is a little short, I would have liked more more more!! :-)

...with a rebel yell?

Re:Complexity is relevant.

[askegg]

People may be more complex than a neuron, but not nearly as complex as the total and their possible interactions. With billions of neurons, each interacting with 1,000 to 10,000 others the possible configurations are enormous, yet most we do not act in such a wildly differing manners. I don't know much about chaos theory, but it mentions something along the lines of the sinple behaviour of complex systems and the complex behaviour of simple systems. Thinking deeper, I am not sure which category this falls into.

Wow! This is Unix!

[Speare]

Wow, this is Unix! I know this!!
--Lex

Large state spaces

[GileadGreene]

Something along similar lines is Frank van Ham's work on visualizing large state spaces. He's generated some neat visualizations of complex transition systems associated with various protocols.

Everywhere????

[Itninja]

Complexity is everywhere

Isn't that kind of subjective? I mean, what's simple to one person, could be incredibly complex to someone else. And as a side thought, does this mean that simplicity is no where?

visualizing large-scale information

[Nick Mitchell]

as far as I can tell, the article only gives one quantification of the scale these folks are dealing with: on the order of tens of thousands for that one case. is this what is considered large? the point of visualizations is to show patterns of nodes (and patterns of paths) in graphy structures. at some point, one runs into one or the other of various limits:

1. pixels on the display: 2 million or so.
2. insufficiency of the clustering algorithms: showing one pixel per node and random placement, or placement by DFS traversal? for trees, or for graphs where classification is the primary concern, then tree-map or "Csoft" views scale relatively well in this regard, but what about for more general problems?
3. implementations (or algorithms) that don't scale: e.g. graphviz uses n^2 (n=#nodes) space for its graph layout!

one must always think about the summarization criteria: what aren't you going to show? how will you indicate that summarization has occured? how do you denote drill-down capability? what will the form of drill-down be? what heuristics should you use to selectively deaggregate, in order to highlight potentially interesting subgraphs? for large-scale info, this is as important as what you will be showing, and how it will be shown! for our stuff, we have graphs with tens of millions of nodes.

visual complexity

[BReflection]

http://www.visualcomplexity.com/

The point of visualization

[espressojim]

The point of visualizing data is to learn something that you could not do with the raw data. In all of the cases shown in the article (yes, I acually read TFA), I didn't spot an example where it actually showed anything useful.

The first example with proteins: how similar are two proteins? If two shapes are similar (and please, how many proteins where being graphed there? One, two, five?), then you might be able to recognize it. If they are similar shapes, are they always presented in the same orientation in space? Does color have any meaning? Does this graph have any legend? If I gave someone who understood the graphs two proteins, what could he say besides "these are related" and "these are not related"? We already have wonderful programs to compare two proteins and say how similar they are two each other, along with being able to the estimate significance of the measurement.

I'm not sure that the other graphics look more informative. They are all pretty, but if they do not convey information (and not lose a large amount of relevant information), then they are just a nice way to generate patterns for some nerd's tie.

Here is it:

[megaditto]

Dr. Wolfram (of Mathematica) offers PDFs of his book for free here (or pay $60 for hardcopy):

http://www.wolframscience.com/thebook.html

I do suggest you at least glance over the first few chapters, look at the pictures.

Also note that the guy got his PhD in Physics at the age of 18 I believe.

Re:Here is it:

[NichG]

Honestly, of the things that bother me about his book, that's not horribly high on the list. The main problem is, nothing he talks about has any ability to predict behavior either qualitatively or quantitatively.

He makes no mention about how to crossover from a microscopic theory to his cellular automata stuff, so even if you can say 'wow, that looks like seashells' when you're presented with some new physical problem you can't just look up his book and figure out what the equivalent CA model would be.

And he doesn't really cover in any depth the intrinsic qualities of doing things with a highly discretized model compared to continuum modelling. Discretization produces a lot of structure in its own right, and that structure may interfere with certain symmetries that the real system has - e.g. translation invariance, invariance when going to a moving frame of reference, and conservation laws. As such, these models tend to give you things which are highly unstable to noise (Conway's game of life collapses to interlocking horizontal and vertical stripe patterns if you add the slightest bit of noise for instance), or work because things exist within the CA model that actually recover those symmetries (but detecting if you're in the first or second case is again something that needs to be covered) - the spiral defect chaos CA models are an example of this, where you essentially recover some sort of continuum dynamics and the discretization doesn't kill it.

I certainly have respect for the method of CA modelling. It can be incredibly useful in simplifying simulation, especially in the case where the full continuum approach ends up having operators which are very numerically unstable. If you can write a simple CA model for resolving the function of those operators, it can save you a ton of time. But I don't really feel that Wolfram's book gives one the necessary set of tools to do that sort of work. Rather, it might just give you an idea to try to do things that way, which is not a bad thing. It just means that even comparing this to peer-reviewed journal publications isn't meaningful because thats not the sort of publication it is. It's more of a halfway-between of a popular science book and a textbook.

A picture speaks louder...

[Cicero382]

...than a thousand words.

Really, you'd be amazed at how even the simplest graphical interpretation of complex data can really show up points of interest. And it's not difficult to see why: Humans' primary sense is visual and we have evolved some seriously complex neural algorithms to interpret visual data.

A simple graph is a case in point. Now take a large amount of complex data and apply just about any process you care to name to present a graphical representation and you can easily see the overall picture.

A very simple example which illustrates statistical clustering. Even with totally random numbers, you *will* find islands of apparently significant populations. This is a common counter-claim to action groups who claim, say, a correlation between mobile 'phone masts and incidents of child leukaemia*. Anyway:

Generate a stream of random numbers and assign a symbol for n = 0.5, display the symbols in a grid and, hey presto! Look at those clusters!

On a more positive note:

We often use graphical representation in our work. This ranges from CTK representations of molecules we're looking at (xlation - pretty pictures with balls and lines) to grid based colour indexed representation of multi-dimentional data sets. In each case the point is to present data in a way that we humans can quickly spot potential areas of interest and get a "feel" for the data we're looking at.

It's all good stuff. (Sometimes very pretty, too)

* Actually, this is a good example of why I'm always wary of purely statistical "proofs". In this case the *science* (ie. proposed mechanisms for this) don't hold up to current understanding.