I have been reading quite a bit graph data structures lately, as I have intentions of writing my own UML tool. As far as I can see, what I want can be modeled as a simple graph consisting of vertices and edges. Vertices will have a few values, and will so best be represented as objects. Edges does not, as far as I can see, need to be neither directed or weighted, but I do not want to choose an implementation that makes it impossible to include such properties later on.
Being educated in pure object oriented programming, the first things that comes to my mind is representing vertices and edges by classes, like for example:
Class: Vertice
- Array arrayOfEdges;
- String name;
Class: Edge
- Vertice from;
- Vertice to;
This gives me the possibility to later introduce weights, direction, and so on. Now, when I read up on implementing graphs, it seems that this is a very uncommon solution. Earlier questions here on Stack Overflow suggests adjacency lists and adjacency matrices, but being completely new to graphs, I have a hard time understanding why that is better than my approach.
The most important aspects of my application is having the ability to easily calculate which vertice is clicked and moved, and the ability to add and remove vertices and edges between the vertices. Will this be easier to accomplish in one implementation over another?
My language of choice is Objective-C, but I do not believe that this should be of any significance.
Here are the two basic graph types along with their typical implementations:
Dense Graphs:
Adjacency Matrix
Incidence Matrix
Sparse Graphs:
Adjacency List
Incidence List
In the graph framework (closed source, unfortunately) that I've ben writing (>12k loc graph implementations + >5k loc unit tests and still counting) I've been able to implement (Directed/Undirected/Mixed) Hypergraphs, (Directed/Undirected/Mixed) Multigraphs, (Directed/Undirected/Mixed) Ordered Graphs, (Directed/Undirected/Mixed) KPartite Graphs, as well as all kinds of Trees, such as Generic Trees, (A,B)-Trees, KAry-Trees, Full-KAry-Trees, (Trees to come: VP-Trees, KD-Trees, BKTrees, B-Trees, R-Trees, Octrees, …).
And all without a single vertex or edge class. Purely generics. And with little to no redundant implementations**
Oh, and as if this wasn't enough they all exist as mutable, immutable, observable (NSNotification), thread-unsafe and thread-safe versions.
How? Through excessive use of Decorators.
Basically all graphs are mutable, thread-unsafe and not observable. So I use Decorators to add all kinds of flavors to them (resulting in no more than 35 classes, vs. 500+ if implemented without decorators, right now).
While I cannot give any actual code, my graphs are basically implemented via Incidence Lists by use of mainly NSMutableDictionaries and NSMutableSets (and NSMutableArrays for my ordered Trees).
My Undirected Sparse Graph has nothing but these ivars, e.g.:
NSMutableDictionary *vertices;
NSMutableDictionary *edges;
The ivar vertices maps vertices to adjacency maps of vertices to incident edges ({"vertex": {"vertex": "edge"}})
And the ivar edges maps edges to incident vertex pairs ({"edge": {"vertex", "vertex"}}), with Pair being a pair data object holding an edge's head vertex and tail vertex.
Mixed Sparse Graphs would have a slightly different mapping of adjascency/incidence lists and so would Directed Sparse Graphs, but you should get the idea.
A limitation of this implementation is, that both, every vertex and every edge needs to have an object associated with it. And to make things a bit more interesting(sic!) each vertex object needs to be unique, and so does each edge object. This is as dictionaries don't allow duplicate keys. Also, objects need to implement NSCopying. NSValueTransformers or value-encapsulation are a way to sidestep these limitation though (same goes for the memory overhead from dictionary key copying).
While the implementation has its downsides, there's a big benefit: immensive versatility!
There's hardly any type graph that I could think of that's impossible to archieve with what I already have. Instead of building each type of graph with custom built parts you basically go to your box of lego bricks and assemble the graphs just the way you need them.
Some more insight:
Every major graph type has its own Protocol, here are a few:
HypergraphProtocol
MultigraphProtocol [tagging protocol] (allows parallel edges)
GraphProtocol (allows directed & undirected edges)
UndirectedGraphProtocol [tagging protocol] (allows only undirected edges)
DirectedGraphProtocol [tagging protocol] (allows only directed edges)
ForestProtocol (allows sets of disjunct trees)
TreeProtocol (allows trees)
ABTreeProtocol (allows trees of a-b children per vertex)
FullKAryTreeProtocol [tagging protocol] (allows trees of either 0 or k children per vertex)
The protocol nesting implies inharitance (of both protocols, as well as implementations).
If there's anything else you'd like to get some mor insight, feel free to leave a comment.
Ps: To give credit where credit is due: Architecture was highly influenced by the
JUNG Java graph framework (55k+ loc).
Pps: Before choosing this type of implementation I had written a small brother of it with just undirected graphs, that I wanted to expand to also support directed graphs. My implementation was pretty similar to the one you are providing in your question. This is what gave my first (rather naïve) project an abrupt end, back then: Subclassing a set of inter-dependent classes in Objective-C and ensuring type-safety Adding a simple directedness to my graph cause my entire code to break apart. (I didn't even use the solution that I posted back then, as it would have just postponed the pain) Now with the generic implementation I have more than 20 graph flavors implemented, with no hacks at all. It's worth it.
If all you want is drawing a graph and being able to move its nodes on the screen, though, you'd be fine with just implementing a generic graph class that can then later on be extended to specific directedness, if needed.
An adjacency matrix will have a bit more difficulty than your object model in adding and removing vertices (but not edges), since this involves adding and removing rows and columns from a matrix. There are tricks you could use to do this, like keeping empty rows and columns, but it will still be a bit complicated.
When moving a vertex around the screen, the edges will also be moved. This also gives your object model a slight advantage, since it will have a list of connected edges and will not have to search through the matrix.
Both models have an inherent directedness to the edges, so if you want to have undirected edges, then you will have to do additional work either way.
I would say that overall there is not a whole lot of difference. If I were implementing this, I would probably do something similar to what you are doing.
If you're using Objective-C I assume you have access to Core Data which would be probably be a great place to start - I understand you're creating your own graph, the strength of Core Data being that it can do a lot of the checking you're talking about for free if you set up your schema properly
Related
I am in a serious need of optimization of my some Unity projects and i have so many objects which are from 3DsMax, so i am wondering if Combining the meshes would have any effect on the memory/performance or i should leave the objects Instance to each other as it would save me some space.
This arise the question that what is the difference between Combined mesh objects or Instance Objects as it will save a lot of memory and hassle if one realy knows the difference and what is better
Looking forward for some Brief information about the two
Thanks
Combining is useful if you have a lot of unique assets that only appear once or twice in a scene, e.g unique buildings in a 3D FPS, but not cloned houses in a SimCity style game. If you have a model that appears many times in a scene it's more performant to have Unity (automatically) batch them, this is Unity's default behaviour. e.g lets say your scene is in an art gallery; if the gallery contains a dozen distinct sculptures then combine them. If it contains a dozen of the same sculpture don't bother, Unity will batch them for you.
However, you should be wary of using different materials, each material adds to the draw count. So, if you had 10 of the same model but using 5 different materials it's going to be expensive. The way round this is to use a texture atlas with a single material, with different UV mapping for each models. This means you have a lot of different models, but save on render time due to the single material.
Also, be aware that transparent shaders much more expensive than opaque, if you have three semi transparent objects in front of each other that's at least 4 render passes.
As you probably know this is a complex subject with a lot of variables (many more than I can describe here) and is best judged by using the profiler.
Here are some general rules of thumb I've learned while creating a game for mobile which naturally is performance critical:
Use as few a materials as possible
Use as fewer textures as possible, share textures between materials
Recycle models as often as possible. Often a model oriented at a different angle or in a different material can look like a whole new model to the player, particularly if their attention is elsewhere in the game
Use LODS extensively
Ensure your models are clean, remove all unnecessary vertices before importing
After importing think if there's anything about the model that could be represented with less vertices
Good use of normal mapping can pay off, depending on the platform. If you can trade in 1000 verts for a 256 px normal map and 50 verts then do it, otherwise dont bother normal mapping just to save a few verts
I created a tutorial that explains draw calls, static batching, lightmapping etc.
https://www.youtube.com/watch?v=x0t2xylbTo8&t=253s
I mean, the basics..
1) I have seen in the Online videos, that they are modelling a character (or anything) through one object only, they are extruding, loop cut, scaling, etc and model a character, why don't they design different objects separately (like hands separately, legs separately, body separate and then join them together and make one object)..??????
2) Like What the texturing department has to see so that they should not return the model back to the modelling department. I mean like the meshes(polygons) over the model face must be quad, etc not triangle. while modelling a character..
what type of basics i should know , means is there any check list or is there any basics which i should see before modelling a character..
Please correct me if i am wrong , and answer my both questions.. Thanks
It may be common but it definitely isn't mandatory to have a model as one solid mesh. Some models will have parts of the body underneath clothing removed to reduce the poly count. How the model is to be used will be a big factor to how you model it, that is a for a single image it is easy to get away with multiple parts, while a character that will be animated in a cartoony animation could be stretched and distorted in ways that could show holes in a model with multiple pieces. When working in a team, there may be rules in place determining whether a solid or multi-part model is considered acceptable.
An example of an animated model made from multiple parts is Sintel, the main character in the Sintel short animation.
There is nothing stopping you from making a library of separate body parts and joining them together when you make your model. Be aware that this can bring complications, if you model an arm with 12 verts and then you make your hand with 15, then you have to fiddle around to merge them together.
You will also find some extra freedom to work with multiple body parts during the sculpting phase as you are creating a high density mesh that is used as a template to model a clean mesh over. This step is called retopology.
It is more likely that the rigging department will send a model back for fixing than the texturing department. When adding a rig and deforming the mesh in different ways, any parts that deform badly will be revealed and need fixing.
[...] (like hands separately, legs separately, body separate and then
join them together and make one object) [...]
Some modelers I know do precisely this and they do it in a way where they block in the design using broad primitive shapes, start slicing some edge loops and add broad details, then merge everything together, then sculpt it a bit further with high-res sculpting tools, and finally retopologize everything.
The main modelers I know who do this, however, model in a way that tries to adhere as close as possible to the concept artist's illustration. They're not creating their own models from scratch but are instead given top/front/back/side illustrations of a character, for example, and are just trying to match it as closely as possible.
When you start modeling everything in small pieces, it helps to have that concept illustration since you can get lost in the topology otherwise and fusing organic meshes together can be difficult to do in a clean way.
[...] why don't they design different objects separately? [...]
Again they sometimes do, but one of the appeals of creating organic meshes by keeping it seamless the entire time is that you can start to focus on how edge loops propagate across the entire model. It helps to know that the base of a finger is a hexagon, for example, in figuring out how to cleanly propagate and terminate the edge loops for a hand, and likewise have a strategy for the hand to cleanly propagate and terminate edge loops as it joins into the forearm.
It can be hard to get the topology to match up cleanly if you designed everything in small pieces and then had to figure out how to merge it all together. Polygonal modeling is very topology-oriented. It tends to require as much thinking about the wireframe and edge flows as it does the shape of the model, since it needs to be a certain way for everything to subdivide cleanly and smoothly and animate predictably with subdivision surfaces.
I used to work with developers who took one glance at the topology-dominated workflow of polygonal modeling and immediately wanted to jump to seeking alternatives, like voxel sculpting. With voxels you could be able to potentially model everything in pieces and foose it all together in a nice and smooth organic way without thinking about topology whatsoever.
However, that loses sight of the key appeal of polygonal meshes. Their wire flow forms a control lattice with a very finite number of control points for the artist to animate and move around to predictably control the shape of their model. You immediately lose that with a voxel representation -- so while voxels free the artist of thinking about how the topology works and how the wireframe flows through the model, it also loses all those control benefits of having that. So often if people use voxel sculpting, they end up meticulously retopologizing everything at the end anyway to gain back that level of coarse and predictable control they have with polygonal meshes.
I mean like the
meshes(polygons) over the model face must be quad, etc not triangle.
while modelling a character..
This is all in the context of subdivision surfaces: the most popular of which are variants of catmull-clark. That favors quads to get the most predictable subdivision. It's much easier for the artist to predict how everything will look like and deform if they favor, as much as possible, uniform grids of quadrangles wrapped around their model with 4-valence vertices and every polygon having 4 points. Then only in the case where they kind of need to "join" these quad grids together, they might create some funky topology: a 5-valence vertex here, a 3-valence vertex there, a 5-sided polygon here, a triangle there -- but those cases tend to deform a bit unpredictably (at least unintuitively), so artists tend to try to avoid these as much as possible.
Because when artists model polygonal meshes in this way, they are not just trying to create a statue with a nice shape. If that's all they wanted to do, they'd save themselves a lot of grief avoiding dealing with things in terms of individual vertices/edges/polygons in the first place and using something like Sculptris. Instead they are designing not only shapes but also designing a control lattice, a wire flow and a set of control points they can easily move around in the future to get predictable behavior out of their control cage. They're basically designing controls or an "interactive GUI/rig" almost for themselves with how they design the topology.
2) Like What the texturing department has to see so that they should
not return the model back to the modelling department.
Generally how a mesh is modeled in a direct sense shouldn't affect the texture department's work much at all if they're working with UV maps and painting textures over them (at that point it doesn't really matter if a model has clean wire flows or not, since all the texture artists do is pain images over the 2D UV map or directly onto the 3D model).
However, if the modeler does the UV mapping, then regardless of whether he uses quad meshes and clean wire flows or not, if the UV mapping is poor, then the resulting texture images will look all distorted. So the UV maps need to be made well with minimal distortion, though that's usually easy to do automatically these days.
The other exception is if the department doesn't use UV maps and instead uses, say, PTex from Disney. PTex really favors quads. In the original paper at least, it only worked with quads.
I was trying to make a comparison between these two technologies when approaching this and I was wondering if any of you already have some experience dealing with any or both of them?
I am mainly interested in performance numbers when dealing with similar use cases.
The difference between the two concepts is the difference between global and local indexing.
As I understand it, Neo4j vertex labels allow you to break up your index space by "categories" of vertices. In this way, a O(log(|V|)) lookup is now an O(log(|V|/c)), where c is the number of categories/labels you have over your vertex set and (the equation) assumes an equal number of vertices in each category. As such, vertex label aid in global index calls as this is a function of V.
Next, Titan's vertex-centric indices sort and index the incident edges of a vertex. The cost to find a particular edge by its label/properties incident to a vertex is O(log(inc(v))), where inc(v) is the size of the incident edge set to vertex v. As such, vertex-centric indices are local indices as this is a function of v.
As I understand it, Neo4j does not support vertex-centric indices. You see this concept currently in Titan, OrientDB, and TinkerGraph (…and RDF stores sort in this manner as well -- via spog pairings). Next, all known graph databases support global indices though, (I believe only Neo4j and OrientDB), support a vertex set partition via the concept of a label.
Again, assuming my assumptions are correct about the use of vertex labels in Neo4j, we are talking about two different use cases — global vs. local indexing. From the perspective of the supernode problem, global indices do not quell the issue of traversing through a large vertex, while this is the sole purpose of the local vertex-centric indices.
You can read about the supernode problem and vertex-centric indices here:
http://thinkaurelius.com/2012/10/25/a-solution-to-the-supernode-problem/
Agreeing with everything Marko said, one could take it further and argue that in the graph database world local indexes can (and even should) substitute global ones. In my opinion, the single greatest advantage of a graph data model is that it lets you encode your data model into the graph topology, gaining qualitative advantages in terms of flexibility, ease of evolution and performance. With this in mind, I'd argue that labels in Neo4j actually detract from all this; reifying a label into a node with adjacent edges pointing to the source having that label is much more in line with the "schema is the graph" philosophy.
Of course, if your engine lacks local indexes we are back at the supernode problem. But if you do have them (something which I'd say should be a requirement for something to be called a graph database), you can easily transform your label into a node L, and create relationships pointing to that node for those vertices which you want labeled with L
v -[L]-> L
meaning that v has label L. Now if you want this in Titan to behave like a Neo4j label, just make the -[L]-> relation to be "manyToOne" (see Titan cardinality constraints) and create a vertex-centric index. This pattern lets you get everything that you could with labels and much more; you can
effectively use this as a namespace for properties relating to that label
sort your elements inside one label
nest labels easily without losing performance (just use a composite key)
separate the declaration of a label L with how elements labeled with it are accessed
Labels may afford some design patterns that improve performance by de-densifying the graph. For example: they eliminate the need for type nodes, which can often get quite dense. Labels can optionally be associated with a unique index. Here, the ability to index a property isn't new, but the ability to constrain it uniquely is. If you were previously doing work in your application, you may experience some performance gains by letting the database handle this. (It's certainly much more convenient to do so.) Finally, if you don't assign a unique index to a label, it will still be indexed, in order to help performance for certain kinds of queries (e.g. "give me all of the nodes having label ")
All that said, while labels may help with performance in certain cases, they were introduced more with ease-of-use in mind. We're just getting started with Neo4j 2.1, which specifically addresses dense node performance (something I know you've been waiting for), along with other performance & scalability improvements... including removing (for all practical purposes eliminating) the upper size limits.
Philip
This question somewhat overlaps knowledge on geospatial information systems, but I think it belongs here rather than GIS.StackExchange
There are a lot of applications around that deal with GPS data with very similar objects, most of them defined by the GPX standard. These objects would be collections of routes, tracks, waypoints, and so on. Some important programs, like GoogleMaps, serialize more or less the same entities in KML format. There are a lot of other mapping applications online (ridewithgps, strava, runkeeper, to name a few) which treat this kind of data in a different way, yet allow for more or less equivalent "operations" with the data. Examples of these operations are:
Direct manipulation of tracks/trackpoints with the mouse (including drawing over a map);
Merging and splitting based on time and/or distance;
Replacing GPS-collected elevation with DEM/SRTM elevation;
Calculating properties of part of a track (total ascent, average speed, distance, time elapsed);
There are some small libraries (like GpxPy) that try to model these objects AND THEIR METHODS, in a way that would ideally allow for an encapsulated, possibly language-independent Library/API.
The fact is: this problem is around long enough to allow for a "common accepted standard" to emerge, isn't it? In the other hand, most GIS software is very professionally oriented towards geospatial analyses, topographic and cartographic applications, while the typical trip-logging and trip-planning applications seem to be more consumer-hobbyist oriented, which might explain the quite disperse way the different projects/apps treat and model the problem.
Thus considering everything said, the question is: Is there, at present or being planned, a standard way to model canonicaly, in an Object-Oriented way, the most used GPS/Tracklog entities and their canonical attributes and methods?
There is the GPX schema and it is very close to what I imagine, but it only contains objects and attributes, not methods.
Any information will be very much appreciated, thanks!!
As far as I know, there is no standard library, interface, or even set of established best practices when it comes to storing/manipulating/processing "route" data. We have put a lot of effort into these problems at Ride with GPS and I know the same could be said by the other sites that solve related problems. I wish there was a standard, and would love to work with someone on one.
GPX is OK and appears to be a sort-of standard... at least until you start processing GPX files and discover everyone has simultaneously added their own custom extensions to the format to deal with data like heart rate, cadence, power, etc. Also, there isn't a standard way of associating a route point with a track point. Your "bread crumb trail" of the route is represented as a series of trkpt elements, and course points (e.g. "turn left onto 4th street") are represented in a separate series of rtept elements. Ideally you want to associate a given course point with a specific track point, rather than just giving the course point a latitude and longitude. If your path does several loops over the same streets, it can introduce some ambiguity in where the course points should be attached along the route.
KML and Garmin's TCX format are similar to GPX, with their own pros and cons. In the end these formats really only serve the purpose of transferring the data between programs. They do not address the issue of how to represent the data in your program, or what type of operations can be performed on the data.
We store our track data as an array of objects, with keys corresponding to different attributes such as latitude, longitude, elevation, time from start, distance from start, speed, heart rate, etc. Additionally we store some metadata along the route to specify details about each section. When parsing our array of track points, we use this metadata to split a Route into a series of Segments. Segments can be split, joined, removed, attached, reversed, etc. They also encapsulate the method of trackpoint generation, whether that is by interpolating points along a straight line, or requesting a path representing directions between the endpoints. These methods allow a reasonably straightforward implementation of drag/drop editing and other common manipulations. The Route object can be used to handle operations involving multiple segments. One example is if you have a route composed of segments - some driving directions, straight lines, walking directions, whatever - and want to reverse the route. You can ask each segment to reverse itself, maintaining its settings in the process. At a higher level we use a Map class to wire up the interface, dispatch commands to the Route(s), and keep a series of snapshots or transition functions updated properly for sensible undo/redo support.
Route manipulation and generation is one of the goals. The others are aggregating summary statistics are structuring the data for efficient visualization/interaction. These problems have been solved to some degree by any system that will take in data and produce a line graph. Not exactly new territory here. One interesting characteristic of route data is that you will often have two variables to choose from for your x-axis: time from start, and distance from start. Both are monotonically increasing, and both offer useful but different interpretations of the data. Looking at the a graph of elevation with an x-axis of distance will show a bike ride going up and down a hill as symmetrical. Using an x-axis of time, the uphill portion is considerably wider. This isn't just about visualizing the data on a graph, it also translates to decisions you make when processing the data into summary statistics. Some weighted averages make sense to base off of time, some off of distance. The operations you end up wanting are min, max, weighted (based on your choice of independent var) average, the ability to filter points and perform a filtered min/max/avg (only use points where you were moving, ignore outliers, etc), different smoothing functions (to aid in calculating total elevation gain for example), a basic concept of map/reduce functionality (how much time did I spend between 20-30mph, etc), and fixed window moving averages that involve some interpolation. The latter is necessary if you want to identify your fastest 10 minutes, or 10 minutes of highest average heartrate, etc. Lastly, you're going to want an easy and efficient way to perform whatever calculations you're running on subsets of your trackpoints.
You can see an example of all of this in action here if you're interested: http://ridewithgps.com/trips/964148
The graph at the bottom can be moused over, drag-select to zoom in. The x-axis has a link to switch between distance/time. On the left sidebar at the bottom you'll see best 30 and 60 second efforts - those are done with fixed window moving averages with interpolation. On the right sidebar, click the "Metrics" tab. Drag-select to zoom in on a section on the graph, and you will see all of the metrics update to reflect your selection.
Happy to answer any questions, or work with anyone on some sort of standard or open implementation of some of these ideas.
This probably isn't quite the answer you were looking for but figured I would offer up some details about how we do things at Ride with GPS since we are not aware of any real standards like you seem to be looking for.
Thanks!
After some deeper research, I feel obligated, for the record and for the help of future people looking for this, to mention the pretty much exhaustive work on the subject done by two entities, sometimes working in conjunction: ISO and OGC.
From ISO (International Standards Organization), the "TC 211 - Geographic information/Geomatics" section pretty much contains it all.
From OGS (Open Geospatial Consortium), their Abstract Specifications are very extensive, being at the same time redundant and complimentary to ISO's.
I'm not sure it contains object methods related to the proposed application (gps track and waypoint analysis and manipulation), but for sure the core concepts contained in these documents is rather solid. UML is their schema representation of choice.
ISO 6709 "[...] specifies the representation of coordinates, including latitude and longitude, to be used in data interchange. It additionally specifies representation of horizontal point location using coordinate types other than latitude and longitude. It also specifies the representation of height and depth that can be associated with horizontal coordinates. Representation includes units of measure and coordinate order."
ISO 19107 "specifies conceptual schemas for describing the spatial characteristics of geographic features, and a set of spatial operations consistent with these schemas. It treats vector geometry and topology up to three dimensions. It defines standard spatial operations for use in access, query, management, processing, and data exchange of geographic information for spatial (geometric and topological) objects of up to three topological dimensions embedded in coordinate spaces of up to three axes."
If I find something new, I'll come back to edit this, including links when available.
If I have a graph of a reasonable size (e.g. ~100 nodes, ~40 edges coming out of each node) and I want to represent it in R^3 (i.e. map each node to a point in R^3 and draw a straight line between any two nodes which are connected in the original graph) in a way which would make it easy to understand its structure, what do you think would make a good drawing criterion?
I know this question is ill-posed; it's not objective. The idea behind it is easier to understand with an extreme case. Suppose you have a connected graph in which each node connects to two and only two other nodes, except for two nodes which only connect to one other node. It's not difficult to see that this graph, when drawn in R^3, can be drawn as a straight line (with nodes sprinkled over the line). Nevertheless, it is possible to draw it in a way which makes it almost impossible to see its very simple structure, e.g. by "twisting" it as much as possible around some fixed point in R^3. So, for this simple case, it's clear that a simple 3D representation is that of a straight line. However, it is not clear what this simplicity property is in the general case.
So, the question is: how would you define this simplicity property?
I'm happy with any kind of answer, be it a definition of "simplicity" computable for graphs, or a greedy approximated algorithm which transforms graphs and that converges to "simpler" 3D representations.
Thanks!
EDITED
In the mean time I've put force-based graph drawing ideas suggested in the answer into practice and wrote an OCaml/openGL program to simulate how imposing an electrical repulsive force between nodes (Coulomb's Law) and a spring-like behaviour on edges (Hooke's law) would turn out. I've posted the video on youtube. The video starts with an initial graph of 100 nodes each with approximately 1-2 outgoing edges and places the nodes randomly in 3D space. Then all the forces I mentioned are put into place and the system is left to move around subject to those forces. In the beginning, the graph is a mess and it's very difficult to see the structure. Closer to the end, it is clear that the graph is almost linear. I've also experience with larger-sized graphs but sometimes the geometry of the graph is just a mess and no matter how you plot it, you won't be able to visualise anything. And here is an even more extreme example with 500 nodes.
One simple approach is described, e.g., at http://en.wikipedia.org/wiki/Force-based_algorithms_%28graph_drawing%29 . The underlying notion of "simplicity" is something like "minimal potential energy", which doesn't really correspond to simplicity in any useful sense but might be good enough in practice.
(If you have 100 nodes of degree 40, I have some doubt as to whether any way of drawing them is going to reveal much in the way of human-accessible structure. That's a lot of edges. Still, good luck!)