graph theorists's topics - tribe.net

Network Visualization software?

danceslut — Tue, 29 Mar 2005 08:04:54 GMT

For people who've worked in this field, what software do you recommend? In particular, what free or low-cost (<$20/license) software do you recommend? This is not my job, it's a hobby.

I've got the "graphviz" package from AT&T, which works, but I'm perhaps too lazy about doing all the input files by hand - are there any good GUI interfaces for graphviz, or similar program packages?

posted in graph theorists - 5 replies

random graph dynamics

wtsn — Thu, 04 Oct 2007 09:26:05 GMT

i just ordered this book from amazon: http://books.google.com/books?id=Mim7MC_sGC4C
for a seminar course i'm taking on the topic of probability and graphs. we're looking for reading to do when we're done with the book as well. especially any open problems. suggestions?

posted in graph theorists - 0 replies

Capital Letters

karl-uk — Wed, 05 Sep 2007 12:00:31 GMT

You may be familiar with

A,R
B,
C,G,I,J,L,M,N,S,U,V,W,Z
D,O
E,F,T,Y
H
K,X
P,Q

The exact grouping depends on the font. I had to change the grouping after preview, because the font is different from the font I typed in.

Karl

posted in graph theorists - 1 reply

Introduction to the new TOE

Wed, 04 Jan 2006 03:57:46 GMT

The short explanation:

The universe is a graph with two kinds of nodes connected by one-way connections. The two kinds of nodes are: "splits", which have one incoming connection and two outgoing connections; and "joins", with two incoming connections and one outgoing.

Change itself is what moves through the connections from node to node, following the correct directions. When change happens, the nodes aren't changed; only their connections to each other are changed, by being rearranged, with no loose ends left over.

The entire universe is motionless, except where a single "point of change" rearranges connections among some of the nodes near it. The point of change moves from node to node, sometimes rearranging connections as it goes:

When the point of change is at a split, there is a 50-50 chance that it will choose one path or the other to travel to, next. When the point of change is at any node, there is a 50-50 chance that that node will be moved past the one ahead of it, in the direction change moves. When a node is to be repositioned past a split, there is a 50-50 chance of putting it at one continuation or the other.

The node rearrangements are always the simplest possible, moving the fewest connections around to create the new arrangement. Any node moved will always keep a constant connection to one of the nodes it was connected with before, taking that node (and whatever nodes it is connected to) along with it.

The single point of change repeatedly moves through the universe, cycling through it. It enters the universe at the one single entrance, every cycle, and then it randomly wanders around until it finds its way out of the universe, through the one single exit every time.

Because joins have two ways for the point of change to arrive to them, they tend to move through space more than the splits near them. So, in a group of interconnected splits, a join will speed ahead and out of them, tending to purify that group of splits even further.

And similarly, in a group of joins, a split will be displaced backwards in the opposite direction that the point of change moves through there, because all the joins pass the split, making the set of joins more pure.

So, at the entrance to the universe, a nearly pure group of splits has formed, and at the exit of the universe, a nearly pure group of joins has formed. Between those formations is an area with nearly equal concentrations of splits and joins. That is the area where we live. The particles and space that we are made of and can experience are all made of close to equal proportions of splits and joins.

An electron is a group of joins connected to a group of splits in a sort-of hourglass shape. The incoming paths by which the point of change arrives to the electron are mostly through its network of joins, which coalesces the many incoming paths into few. In the center of the electron, there is a clump of nodes with nearly equal concentrations of splits and joins, and then most of the outgoing paths lead out through the other half of the electron, a network of splits leading the point of change back out into the surrounding space.

The two charges, positive and negative, are formed because all the charged particles collaborate to make two realms in the greater, shared space: the realm dominated by paths leading out of and away from negatively charged particles and into positively charged ones; and the other realm, dominated by paths leaving the positive particles, and entering negative ones.

The two charge realms blend into each other. But because the nodes in the outgoing paths of a particle are much more likely to be moved toward an oppositely charged particle's incoming paths, in the same charge realm of space, than toward the other realm of space, (where the particle's own incoming paths are), a charged particle is stuck with the charge it has, because its network of joins is stuck in one realm of space and its network of splits in the other. (Hypothetically, if a particle's incoming and outgoing paths were each set up to straddle the divide, portioned equally between the realms, the particle would soon align one way or the other, when it is tipped off balance randomly.)

Positrons are exactly like electrons, except flipped the other way relative to the two charge realms.

Photons are made of a core of splits which branch out to an ever-expanding sphere of joins. The joins race outward, and the splits "inside" form their own separate space, disjoint from the greater shared space except where their incoming paths are attached, and at and near the joins in the expanding sphere of joins. At the sphere, there is a region made up of a blend of nodes of the photon's network of splits, the joins of the sphere, and the nodes of the greater, shared space.

Joins entering the photon through its incoming paths quickly move out through the network of splits and eventually become part of the sphere as it expands. The closer to the center of the network of splits a join is, the more attention it gets from the point of change when it comes through the photon, and so the faster it travels. (Each split diverts the point of change half the time, on average, halving the attention for a split just behind it.)

Joins of the photon that fall behind the rest of the sphere, by chance, become closer to the center of the network of splits inside the photon, and so get more visits by the point of change, which makes them catch up, or keep pace, with the rest of the sphere.

Most of the sphere of joins oscillates between the charge realms as it travels outward. The sphere of joins moves into and out of one charge realm, and then the other, as it expands. But, oscillating between the realms is a longer journey than travelling along only where the realms meet, where some part of the sphere or another is always forging ahead. And that makes the oscillating parts fall behind the fastest part.

So then, the part that oscillates gets helped by being closer to the center of the photon. How far the oscillating part is allowed to lag behind the forefront, before it gets enough attention from the point of change to keep pace with the rest of the sphere, is determined by how often the point of change comes through the photon, relative to the surrounding space. That is, the more energy a photon has, the less the oscillating part of its sphere lags, and the more times its sphere oscillates between the charge realms as it keeps pace with the fastest moving part of the sphere. This makes a shorter wavelength.

And, the less energy the photon has, the further back the ocsillating part of the sphere lags before it gets enough attention from the point of change to keep pace with the forefront. This makes a longer wavelength.

Energy is the average number of visits to a given node or set of nodes per cycle through the universe, by the point of change, taking into account revisits in the same cycle.

Distance is the number of nodes travelled through to get from somewhere to somewhere else, following the correct directions of the connections. There are many distances between any two places, coming and going, but usually, in the greater shared space, the shortest distances back and forth are close to equal ,except for some relatively few shortcuts, which make quantum entanglement possible. It doesn't matter how far through the shared space a connection seems to stretch - it is still just one step for the point of change, the shortest distance in the universe, which isn't really a distance at all, but a count of one node traversed.

Directions in space are paths through the nodes, following the directions of connections. From a single node's perspective, its connections are separate dimensions. A node "feels" like it's in three dimensions because of its three connections. Every path, of any length, through the nodes would be a separate dimension by itself, except that the paths might branch off and meet each other again, something that dimensions don't do. Also, what looks on paper like a zig-zaggy path through the nodes is, in effect, just another straight path through space from the point of change's perspective.

Angles are determined by how interwoven a set of paths is compared to another. If a set of paths are more interwoven, then they are packed into smaller angles of space. Or another way to look at it is, roughly: if any two paths, of unlimited length, are to be chosen randomly, starting out near the same starting place, what is the chance that the two paths will be chosen such that they intersect? The greater the chance of intersection, the closer the angle is between the two directions.

Momentum is the result of the outgoing paths of an object being more interwoven in some directions than in other directions. Joins of the object move down all the outgoing paths at once, pulling the rest of the object with them in all directions. But those same joins are also what hold the outgoing paths together, making them interwoven. So, where the joins are more concentrated, they pull the paths of that direction into smaller angles. And as the joins move along, they bring together the paths in space just ahead of the object, as they go.

The object is being pulled equally, on average, down each outgoing path. But a higher proportion of those paths are packed into some directions than others. Whereas, the incoming paths to the object are lengthening away from the object as it leaves them behind, but those paths are interwoven equally. The result is that the object feels no force acting on it, but moves constantly through space.

All of space and matter is made of the same thing: fields formed by the space of the web of interconnected splits and joins. Outgoing paths of an object lead away, but also lead back to incoming paths, which lead back to outgoing paths. A path from anywhere to anywhere else can almost always be found. And there are many, many nodes. What ends up mattering from our perspective is the concentration of splits versus joins in an area, and their "pressure", and the probability of them diffusing from one area to another, or in certain directions, perhaps taking formations with them.

Roughly described, when an object, A, bumps another object, B, the formation of joins which ventures ahead of A, interweaving A's outgoing paths and pulling A along, moves into and through B, mostly intact, leaving A behind. Their interconnectedness continues, mostly, depending on the consistency of B, and the direction of paths that they hold together also continues as it moves through B, and they keep their direction of pull. When the joins get to the far end of B, they participate in interweaving B's outgoing paths, compromising on a new direction of travel for B, and then they help pull B along. They never get too far ahead of B, because each join has the two incoming paths which connect back to B and thus they always pull part of B with them if they move, themselves.

Photons are reflected without a transfer of momentum. When enough joins in a local area of the expanding sphere get turned to any other direction, they start an exodus of adjacent parts of the sphere, directly back into the sphere, due to the sphere's cohesiveness. That part of the sphere turns in on itself, with an inverted partial sphere shape, a mirror image, growing and moving into the original sphere, in the direction toward the photon's origin.

Photons are often born from electrons. The clump of nodes in the center of an electron changes size according to the pressure of concentrations of splits and joins in the surrounding space. A change in the concentration and pressure of joins in the space near the electron allows a mass exodus of joins from the clump of nodes in the center of the electron. The joins race out, following the outgoing paths of the electron, and pull a network of splits after them, forming the photon. The oscillation of the photon's sphere is thus calibrated, so the whole sphere moves into one charge realm first.

Protons are two positrons and one electron in very close association, arranged so compactly that they change the space around them, pulling more incoming paths to them, thus increasing their energy/mass.

Example of a node rearrangement at the point of change:

Get a pencil with an eraser.
Draw a node, A. Draw two arrows leading to it and one arrow leading away from it. At the arrow leading away, draw another node, B. Draw another incoming arrow to B, leading from nowhere, and an outgoing arrow from B leading to nowhere. Draw another node, C, at the end of the outgoing arrow from B. Draw another node, D, at the beginning of the arrow leading into B. Draw two arrows leading away from C. Draw another node, E, at one of the arrows from C, and another node, F, from the other arrow from C. ( B is where the point of change is. It arrived from A. Now B is to be moved past C, in the direction of E, taking the node D with it) Erase the arrow from B to C. Erase the arrow from A to B, and redraw it from A to C. Erase the arrow from C to E. Redraw the arrow that used to be from B to C as a new arrow from B to E. Redraw the arrow that used to go from C to E so that it goes from C to B. B has moved, and the new position for the point of change is E.

Questions remain. This is about as far as I've gotten with this. There are particles to figure out, and a whole new field of science describing phenomena mathematically in terms of the random walks through the nodes. Also, some variations in how the node rearrangements are done may yield the same physical results as with how I've described, as seen on the scale of particles. In any case, copy this and send it to anyone, and/or use it to your own heart's content. I am a homeless guy and could use help, but I also don't want to mess with it anymore, and don't want to answer too many questions about it for my whole life, or have to hide from such questions. So, take it, if it's worth it!

posted in graph theorists - 4 replies

Introduction

Sun, 21 Aug 2005 18:45:06 GMT

Hello,

I'm new here and thought I'd introduce myself.

My name is Flemming Madsen and I live in London, UK.

I have a passionate interest in graph theory and network analysis. I'm interested in classical GT problems as well as trying to apply GT in new areas.

In my daytime job I work for a consultancy that applies network analysis to a number of problems, including social network analysis and web-based stakeholder analysis. (More at http://www.Onalytica.com).

In my free time I run a social networking site centred on books. (http://www.ConnectViaBooks.com).

I'm keen to connect with others with an interest in GT.

What are you up to?

Sincerely,
Flemming

posted in graph theorists - 3 replies

Cone Graphs

Waw — Fri, 20 May 2005 01:15:00 GMT

A while ago on Discovery or the Finance channel I saw this EU woman that came up with these Indicators / Conical charts.

The tip of the measurements stems into a whole 3D cone.

Multiple variables allow for a forest of cones.

The beauty was that where various signals intersect the cones overlap and give a clear image of the interference generated by say : data from company A effect on data from company B.

The data can be disected and a see through view of only the intersecting paths extracted, as well as various other not easy noticeable relationships in regular charts...

Can't remember her name or her method or technique name.

ANYONE skilled with advanced graphing ?

qb

posted in graph theorists - 0 replies

Pajek

Tue, 22 Mar 2005 17:50:23 GMT

Any Pajek users out here?

posted in graph theorists - 10 replies

New roads can cause congestion

zby — Fri, 04 Feb 2005 11:14:09 GMT

I think this is should be on topic here: http://www.newscientist.com/article.ns?id=dn6922

posted in graph theorists - 5 replies

visualizing social networks

Jaffa — Tue, 22 Mar 2005 04:40:44 GMT

y'all might be interested in my latest blog post on social networks:
http://www.mobilecommunitydesign.com/archives/000115.php
any thoughts appreciated.

posted in graph theorists - 9 replies

A Comparison of Hyperstructures: Zzstructures, mSpaces, and Polyarchies

zby — Tue, 22 Mar 2005 11:30:00 GMT

Hi,

This is an interesting paper I've read recently: http://www.dgp.toronto.edu/papers/mmcguffin_HT2004.pdf

It reinterpretes user interfaces as graphs leading users to their desired information. It's nice model and it opens many new questions like:
- is the path length leading to the information a good measure for judging the 'goodness' of a model (from mathematical point of view and from psychological point of view)
- what should be the exact definition of what they call 'subsumption' in the paper (a constant factor for the paths lenghts?)

posted in graph theorists - 0 replies

best websites for a beginner

phil — Wed, 09 Feb 2005 15:55:35 GMT

OK, I´m so not a mathematician. And my knowledge of graph theory is pretty much limited to a couple of exercises on algorithms to find Euler cycles on my computer science degree.

Anyone got any pointers to sites (or textbooks) for amateurs hoping to get a good overview of this field?

cheers

phil

posted in graph theorists - 2 replies

areas of study

Ben — Thu, 10 Jun 2004 02:53:36 GMT

I just aced the final for my first graph theory class. The class was loads of fun. From what I've seen, graph theory can go in many many directions. Some areas of study involve more statistics type stuff, such as in personal networks. Some seem like analyses of really specific problems, like pebbling and pegging. I'm thinking about studying graph theory as a grad student, and I'm wondering about people's experiences with various fields. What is out there to study?

posted in graph theorists - 7 replies

New tribe for R

harolddd — Mon, 07 Jun 2004 01:43:53 GMT

New tribe for R

Started a tribe to discuss, share tips and code for the open-source "R" statistical programming enviromment. Please join if you use R or are interesting in learning about it.

r-statisticalenvironment.tribe.net

www.tribe.net/tribe/servl...emplate/pub%2CTribeCard.vm

Harold

posted in graph theorists - 0 replies

ties?

Tapani — Thu, 25 Mar 2004 14:13:47 GMT

Hello,
<br>
<br>I'm a new here. I would like to hear about your experiences from internet communities. Have you ever felt that you have really been part of a community in the virtual world? How was it? When you can say that there is a community or a tie? I'm not sure that if I have had some conversation with someone in a news group then there is a tie. What do you think? Tie as a theoretical link in a graph is not the some as a social relationship?
<br>
<br>Tapani

posted in graph theorists - 0 replies

stong and weak ties

DUFFMAN — Thu, 15 Jan 2004 01:39:15 GMT

hi - i am new to this tribe.net thing but was glad to find a graph theory group! i am a research fellow at the research center for group dynamics at the institute for social research at the university of michigan. i am using graph theory in some of my work on cross-cultural differences in ego-centered friendship networks. but i have something of a different question. i have been reading a lot about strong and weak ties in the sociological literature. i am wondering if anyone has any opinions about differences in friendship network formation between a site like tribe.net and friendster.com? friendster has none of these tribes that may serve as a source of weak ties in which one may have the opportunity to meet a large number of people, some of whom might become strong ties. friendster, not having such groups and being based more upon strong ties, has less of a dynamic property to it - networks on friendster may be much more stable. has anyone thought about this?

posted in graph theorists - 10 replies

graph layout and graph partitioning

Sat, 29 Nov 2003 15:03:38 GMT

Anyone here interested in these topics? In particular, approaches to the graph layout problem that leverage a partitioning approach, or vice versa?

posted in graph theorists - 11 replies

text analysis

sarahboyd — Mon, 18 Aug 2003 21:03:47 GMT

not graph theory, but interesting, and related:
http://www.nature.com/nsu/030811/030811-9.html

posted in graph theorists - 2 replies

RouteWord

adfm — Sat, 29 Nov 2003 09:32:31 GMT

Hey folks, here's something fun...

http://www.routeword.com/

posted in graph theorists - 1 reply

But can you dance to it?

adfm — Mon, 18 Aug 2003 21:07:09 GMT

http://math.ucsd.edu/~fan/hear/

Reminds me of embeding images in audio. Just what does that bananna sound like? Maybe just like tribe.net ;)

posted in graph theorists - 1 reply

petersen graph fun

Micah — Thu, 14 Aug 2003 14:07:30 GMT

i recently met a math postgrad here in prague who has shown me an interesting proof he came up with that the petersen graph (see the current tribe photo) has no 3 edge coloring. it goes like this: call the three colors 'a', 'b', and 'c'. imagine that you have four edges in the arrangement --< (i hope that ascii art is clear). then, if the leftmost edge has the color, say, 'a', then one of the rightmost edges will also have the color 'a'. now, since the petersen graph has a 5-cycle (the outmost ring on the picture), 'a', 'b', and 'c' must all appear at least once in that cycle. now, if you look carefully, you will see that each edge in this five cycle is involved in in two of the --< widgets, with the non-overlapping < parts belonging to the star in the middle. now, since there is an edge on the outside with color 'a', at least two edges in the center star must also have the color 'a', and the same for 'b' and 'c'. that makes 6 edges total, but there are only five edges in the middle! hence there is no 3 edge coloring. i love elegant stuff like this.

posted in graph theorists - 0 replies

diametric mesh

adfm — Thu, 07 Aug 2003 22:32:32 GMT

Anyone in this group familiar with multi-hop mesh networks?

http://w3.antd.nist.gov/wctg/netanal/netanal_netmodels.html

A star-mesh promotes efficiency through instability (single point of failure), the ring-mesh stability for sake of efficiency, the diametric mesh happily falls somewhere between the two.

Anybody care to chat up my new curiosity?

graph theorists's topics - tribe.net

Network Visualization software?

random graph dynamics

Capital Letters

Introduction to the new TOE

Introduction

Cone Graphs

Pajek

New roads can cause congestion

visualizing social networks

A Comparison of Hyperstructures: Zzstructures, mSpaces, and Polyarchies

best websites for a beginner

areas of study

New tribe for R

ties?

stong and weak ties

graph layout and graph partitioning

text analysis

RouteWord

But can you dance to it?

petersen graph fun

diametric mesh

trickery.