I need to visualize a relatively large graph (6K nodes, 8K edges) that has the following properties:
Distinct Clusters. Approximately 50-100 Nodes per cluster and moderate interconnectivity at the cluster level
Minimal (5-10 inter-cluster edges per cluster) interconnectivity between clusters
Let global edge overlap = The edge overlaps caused by directly visualizing a graph of Clusters = {A, B, C, D, E}, Edges = {Pentagram of those clusters, which is non-planar by the way and will definitely generate edge overlap if you draw it out directly}
Let Local Edge Overlap = the above but { A, B, C, D, E } are just nodes.
I need to visualize graphs with the above in a way that satisfies the following requirements
No global edge overlap (i.e. edge overlaps caused by inter-cluster properties is not okay)
Local edge overlap within a cluster is fine
Anyone have thoughts on how to best visualize a graph with the requirements above?
One solution I've come up with to deal with the global edge overlap is to make sure a cluster A can only have a max of 1 direct edge to another cluster (B) during visualization. Any additional inter-cluster edges between cluster A -> C, A -> D, ... are disconnected and additional node/edges A -> A_C, C -> C_A, A -> A_D, D -> D_A... are created.
Anyone have any thoughts?
Prefuse has some good graph drawing link text algorithms built in and it seems to handle fairly large graphs relatively well. You might try Flow Map Layout which is built on top of Prefuse.
Given your objectives, I think that the Fruchterman-Reingold algorithm does a pretty decent job of preventing edge overlap. See for example this screenshot of a network consisting of multiple components drawn using the Fruchterman-Reingold algorithm. IGraph has built-in support for this algorithm (as does Networkx I believe) and is really fast.
There is a program built on top of Prefuse called SocialAction. You have to request the code from the author, but it does a lot of statistical analysis on the graph for you, such as identifying subgraphs. I've used it on a graph with more than 18,000 nodes, and although it is very slow at that scale it still works.
Although it may be silly to ask at this point, had you tried out http://www.graphviz.org/ ?
I haven't seen too many graph visualization tools that support separating clusters within a graph visually. One option might be to take a look at WilmaScope. It looks to have some support for cluster based layouts.
Organic layout manages fairly well clustered graphs in yFiles framework. Try first in yEd to see if it does what needed. It is probably reasonable to use nested graphs alias groups for each cluster. Organic layout has feature called Group Layout Policy which can be used if layout needs to be done using different principles for inter-cluster and intra-cluster edges, with incremental layouting. With some effort, one can translate graph into GraphML to avoid manual work.
Related
I have a graph that consists of nodes. Each node can have multiple parents and/or children. I want to display that graph and connections between nodes.
But I don't know how to redistribute nodes to maximize readability. Currently I'm facing following problems:
Node connections cross each other too much even though it's unnecessary and can be evaded
Connections between nodes are too long visually
Some connections have the same angle so they overlap and become one line
Connections beteween column i and column i-2 (and further away) sometimes go straight through elements in column i-1
Also I can shift nodes only vertically, not horizontally because the amount of columns is limited.
To make it easier for myself I tried to place nodes in a grid-like pattern. And I've managed to group them by columns. But then I somehow need to iterate through columns and compare them with other columns to re-arrange stuff. And I don't know where to start.
UPD: I may be wrong but I feel like my problem with graph alignment is somehow related to a typical graph problem of the shortest path. Except that in my case there are multiple paths that should be calculated at the same time and some nodes can be passed only once.
On the image below you can see a nearly ideal redistribution that I made by just scribbling stuff on paper (direction left-to-right shows parent-to-child connections).
It is graph layout and drawing problem. You can take one of the following two approaches
Use already existing libraries: There are many graph layout libraries available for example GraphViz, Gephi, D3js etc. You can use theirs APIs directly or you can find applications/tools build on top of them. But to get best layout, you need to have guess on family of layout. e.g. Layered graph layout (Good for dense but layered graph like flowcharts) Tree layout (Used when graph is actually a tree or forest. There are many variants of tree), Radial tree layout (Again for tree but in polar system), Force directed layouts (When you don't know what visual structure will best represent the data, it is good starting point). All these layout will have many customization parameters like spacing between nodes, spacing between nodes and edges, overall aspect ratio of drawing etc.
GraphViz
Gephi
Implement layout algorithms yourself
Detailed coverage of graph drawing algorithms for different families can be found here
Graph Drawing Handbook
If you don't want to get into details, here are quick start points
For graphs, Do a topological sort and place nodes in layers as dictated by topo order. It can give you a very good starting point and help you avoid unnecessary crossings. Grid can be good idea here. But place nodes in grid in topo order.
Alternatively, Find a spanning tree for the graph, use tree layouts to draw spanning tree and then add remaining edges
For trees: Use recursive bottoms up approach for placing subtrees. For radial trees, do rectilinear layout and then transform to polar coordinate system
For unknown family: Use force directed method. Define force between two nodes (e.g. spring force) and then go through iterations to find equilibrium point.
Best auto visualization of a graph is very interesting area and people are trying many ML techniques here.
You could implement force directed drawing. Or you could use a graph drawing library that already supports force directed drawing, such as D3's force directed layout.
I want to visualize a large (tens of thousands of nodes) tree-like structure. The graph is almost a hierarchical tree, with the difference that there can be a few extra edges (making it not strictly at tree anymore, potentially making algorythms crash)
What is the best way I can do this?
You might be looking for something like ArcTrees (PDF) or Treemaps with Link Overlays (PDF). For the latter, edge-bundled versions (PDF)have been explored as well. The combination of a space-filling base visualization of the tree and the extra edges being displayed as arcs or links on top of them really helps to show where the tree property breaks down and how many extra edges there are. So, if that is what you are looking for, I'd go with these.
Otherwise, you can always use a standard DAG layout - e.g., as produced by the Sugiyama framework. See this Wikipedia entry for more information on this option.
I have a dataset of DNA relationships (as a percent match) between myself and few hundred relatives, almost all distant relatives. I also have data on DNA relationships between each of them and certain other members in the dataset.
I'm hoping to build a network graph that shows the interrelationships and have Gephi build something that loosely resembles a family tree. But even using a small sample database I can't get the resulting graph to look anything like that.
I want each relationship (i.e. edge) to have a "force" related to the closeness of the relationship, so distant relatives (nodes) are pushed further away. I want the graph to self-assemble based on these "forces" and assume there is a layout for this, but I haven't found one.
I'm currently putting the DNA relationship in the weight column, and not using the interval column at all. But even using just 8 relatives and artificially perfect data I have to manually move nodes around to make it look remotely useful.
What layout should I use for this type of graph, and what other advice can you offer to make this work? Should the weight field increase or decrease as relationship distance increases?
… and have Gephi build something that loosely resembles a family tree. But even using a small sample database I can't get the resulting graph to look anything like that.
A family tree connects descendants (mostly). DNA similarity (as a percentage) does not conform to this structure. Related questions may be answered here.
Setting a Library > Edges > Edge Weight -filter to the DNA similarity attribute may help (but will not produce "something that loosely resembles a family tree").
I want each relationship (i.e. edge) to have a "force" related to the closeness of the relationship, so distant relatives (nodes) are pushed further away. I want the graph to self-assemble based on these "forces" …
All layouts work like that. However, Gephi does not feature hierarchical positioning. 3rd party candidates include EventGraphLayout, Layered Layout and Concentric Layout.
Should the weight field increase or decrease as relationship distance increases?
The greater an edge's weight, the stronger its connection (resulting in less distance between the nodes it connects). To a family tree however this is irrelevant.
I'm hoping to build a network graph that shows the interrelationships between each member …
What layout should I use for this type of graph, and what other advice can you offer to make this work?
Following steps emphasize clustering and modularity:
Calculate modularity.
Color nodes by modularity class: Appearance > Nodes > Partition > Modularity Class
Apply a layout; ForceAtlas 2 for example (with Dissuade Hubs, LinLog mode and Prevent Overlap enabled).
Apply the Contraction layout afterwards if necessary. Optionally set node size according to (for example) Eigenvector Centrality (prior to applying layout).
I have started to work with gephi to help me display a dataset.
The dataset contains:
tags (terms for a certain picture) as nodes
Normalized Google Similarity Distance between those tags as edges with a weight (between 0 und 1)
Every tag is connected to every other tag, as long as they both belong to the same picture. So I have one cluster of nodes and edges for every picture.
I have now imported this dataset to gephi in the following format:
nodes: id, label
edges: target, source, weight (between 0 and 1)
Like 500 nodes and 6000 edges.
My problem now is that after importing all those nodes and edges the graph looks kind of bunched with no real order. Every cluster of every picture is mixed into other clusters of other pictures.
Now using Modularity as Partition algorithm (which should use the Louvain method) the graph is getting colored, each color represent a picture. Now I can split this mess, using the Force Atlas 2 Layout.
I now have a colored graph with something like 15 clusters (every cluster represent 1 picture)
Now I want to cluster those clusters again using tags (nodes) according to their Normalized google distance (weight of the edges), which should then be tags which are somewhat equal in their meaning.
I hope you guys understand what I want to accomplish.
I can also upload a picture to clarify it.
Thanks a lot
I don't think you can do that with the standard version of Gephi. You would need to develop a plugin to implement the very last step of your process.
Gephi is good for visualizing and browsing graphs, but (for now) there are more complete tools when it comes to processing topological properties. for instance, the igraph library (available in C, R and python) might be more appropriate for you. And note that you can use a file format compatible with both Gephi and igraph, which allows you to use both tools on the same data.
I was able to solve my problem. I had to import every one of these 15 clusters on their own. In this way i could use the Modularity method on just those few.
NetworkX is mostly for graph analysis, PyGraphviz mostly for drawing, and they're designed to work together. However, there's at least one respect in which NetworkX's graph drawing (via MatPlotLib) is superior to PyGraphviz's graph drawing (via Graphviz), namely that NetworkX has a spring layout algorithm (accessible via the spring_layout function) specifically for directed graphs while PyGraphviz has several spring layout algorithms (accessible via the neato program, and others) that lay out directed graphs as if they were undirected graphs. The only Graphviz / PyGraphviz layout program that really handles direction in a graph is dot, but dot creates hierarchical layouts, not force-directed layouts.
Here is an example that shows the difference between NetworkX and PyGraphviz for spring layouts of directed graphs:
import networkx as nx
import pygraphviz as pgv
import matplotlib.pyplot as ppt
edgelist = [(1,2),(1,9),(3,2),(3,9),(4,5),(4,6),(4,9),(5,9),(7,8),(7,9)]
nxd = nx.DiGraph()
nxu = nx.Graph()
gvd = pgv.AGraph(directed=True)
gvu = pgv.AGraph()
nxd.add_edges_from(edgelist)
nxu.add_edges_from(edgelist)
gvd.add_edges_from(edgelist)
gvu.add_edges_from(edgelist)
pos1 = nx.spring_layout(nxd)
nx.draw_networkx(nxd,pos1)
ppt.savefig('1_networkx_directed.png')
ppt.clf()
pos2 = nx.spring_layout(nxu)
nx.draw_networkx(nxu,pos2)
ppt.savefig('2_networkx_undirected.png')
ppt.clf()
gvd.layout(prog='neato')
gvd.draw('3_pygraphviz_directed.png')
gvu.layout(prog='neato')
gvu.draw('4_pygraphviz_undirected.png')
1_networkx_directed.png:(http://farm9.staticflickr.com/8516/8521343506_0c5d62e013.jpg)
2_networkx_undirected.png:(http://farm9.staticflickr.com/8246/8521343490_06ba1ec8e7.jpg)
3_pygraphviz_directed.png:(http://farm9.staticflickr.com/8365/8520231171_ef7784d983.jpg)
4_pygraphviz_undirected.png:(http://farm9.staticflickr.com/8093/8520231231_80c7eab443.jpg)
The third and fourth figures drawn are basically identical but for the arrowheads (the whole figure has been rotated, but apart from that, there's no difference). However, the first and second figures are differently laid out - and not just because NetworkX's layout algorithm introduces an element of randomness.
Repeatedly running the code above shows that this is not a chance occurrence. NetworkX's spring_layout function was apparently written on the assumption that if there is an arc from one node to another, the second node should be closer to the centre of the graph than the first (i.e. that if the graph described in edgelist is directed, node 2 should be closer to node 9 than nodes 1 and 3 are, node 6 should be closer to node 9 than node 4 is, and node 8 should be closer to node 9 than node 7 is; this doesn't always work perfectly as we see from nodes 4 and 5 in the first figure above, but that's a small issue compared to getting both 2 and 9 near the centre and the 'error' from my point of view is very slight). In other words, NetworkX's spring_layout is both hierarchical and force-directed.
That is a nice feature, because it makes core/periphery structures more obvious in directed graphs (where, depending on the assumptions you're working with, nodes without incoming arcs can be considered to be part of the periphery even if they have large numbers of outgoing arcs). #skyebend has explained below why most layout algorithms treat directed graphs as if they were undirected, but the graphs above show (a) that NetworkX treats them differently, and (b) that it does so in a principled way that is helpful for analysis.
Can this be replicated using PyGraphviz / Graphviz?
Unfortunately the documentation and the commented source code for NetworkX's spring_layout (actually fruchterman_reingold_layout) function provide no clue as to why NetworkX produces the result that it does.
This is the result of using PyGraphviz to draw the network using the NetworkX spring_layout function (see my own answer to this question below).
5_pygraphviz_plus_networkx.png:
(http://farm9.staticflickr.com/8378/8520231183_e7dfe21ab4.jpg)
Okay, I think I figured it out so I'm going to answer my own question. I don't think it can be done in PyGraphviz per se. However, one can instruct PyGraphviz to take the node positions from NetworkX but peg them (using !) so that the neato program is prevented from actually doing anything except rubber-stamping the node positions calculated by spring_layout. Add the following lines of code to the above:
for k,v in pos1.iteritems():
gvd.get_node(k).attr['pos']='{},{}!'.format(v[0]*10,v[1]*10)
gvd.layout(prog='neato')
gvd.draw('5_pygraphviz_plus_networkx.png')
The result is not perfect -- I had to multiply the co-ordinates by 10 in order to stop the nodes from being drawn on top of each other, which is (obviously) a kludge -- but it's an improvement, i.e. the nodes with 0 indegree are on the outside (benefit of laying out with NetworkX) and there are proper arrowheads that don't get swallowed up by the nodes themselves (benefit of drawing with PyGraphviz).
I am aware that this isn't strictly what I asked for, though (i.e. a solution using PyGraphviz / Graphviz itself).
If somebody can provide a better solution I'll be happy!
EDIT: Nobody's provided a better solution to the problem as articulated above, so I'm going to accept my own answer to signal that it actually works. However, I'm also voting up skyebend's answer because - although it doesn't solve the problem - it's a very useful contribution to understanding the underlying issues.
Graphviz also has an fdp and sfdp layout mode for doing force directed placement of nodes which is analogous to a spring layout. I'm not familiar with NetworkX, but it seems gvu.layout(prog='fdp') might work? If NetworkX allows passing additional arguments to Graphviz there are a number of configurable layout parameters you could tweak that may give you a layout closer to what you want. See Graphviz docs: http://www.graphviz.org/content/attrs
However, the fdp layouts treat the network as an undirected graph. Most 'spring' layouts I know of also treat networks as undirected because they must transform them into a Euclidean space (the screen) in which distances are symmetric. One exception would be 'magnetic' spring layouts which also attempt to align arcs so they are pointing in a similar direction to convey hierarchy, as a sort neato/dot hybrid.
Algorithm implementations may also differ in how they transform the network distances in an directed network to undirected weights/distances to be optimized by the layout. You may want to do this step explicitly yourself if you want more control over the way directed arcs are interpreted.