Some of the links in this post are very cool graphs. Definitely worth checking out!
Summary: Given a graph, finding an important node can sometimes be very intuitive. For example, finding a ‘bridge’ between two separate social groups might be very obvious if the graph is drawn properly. However, converting a set of node-node pairs (edges) into an image is not always intuitive. Here are some links to algorithms, applications, and other useful sites related to drawing graphs.
Visualizing graphs is useful. Patterns in data might be very hard to see until a graph is constructed. Take for example the drastic changes in e-mail correspondent structure at Enron before their collapse. Professor Kathleen Carley, at Carnegie Mellon, analyzed the network activity there: “what you see is that prior to the investigation there is this surge in activity among the people at the top of the corporate ladder.” But, she continues “as soon as the investigation starts, they stop communicating with each other and start communicating with lawyers.” (NY Times, May 21st, 2005) Of course, as we have seen in class, powerful nodes, hubs, and bridges can be found easily if presented in a well organized graph. This is why a growing interest in the field of information visualization [wiki] [@MIT] surrounds the conversion of interesting data into a representative image.
Analysis of the enron e-mail network reveals an anomaly
Indeed, a single graph can be drawn in many different ways [wiki: graph drawing]. Often graph drawing is very intuitive: for example, the nodes can be drawn along the perimeter of a circle, and lines can be drawn between nodes on a edge. However, sometimes a graph should be drawn where no lines cross each other; this is called a planar graph (ex). Other graphs should be drawn to keep ’similar’ nodes as close as possible. Even more complex graph layouts may try to minimize the length of certain edges (when laid out as an image), or simulate edges as physical springs connected to each other [force based layout]. Clearly different layouts are good for different purposes, and some such as the planar graph are impossible to achieve at times. An increasing number applications now exist to draw static (non-changing) graphs as an image (ex: aisee).
Increasingly, non-static graphs are also becoming subjects of interest. A static graph might be a ’snapshot’ of the facebook network at any one time, but often we are also interested in how such a network develops over time: is there triadic closure? if so, how long/frequently does triadic closure occur? are there probabilistic models for how a network might grow? etc. One popular programming package has aimed at visualizing dynamic data is called Processing [link] (ex: State of The Union Addresses, salary vs. performance of U.S. baseball teams). Non-static data, combined with an interactive interface, has certainly grown more and more popular.
Most of the graphs online right now are still static images representing static data, but hopefully that will change soon. In addition to the MIT research linked earlier, Carnegie Mellon has recently began a program in ‘Information Visualization’ which is currently being taught by visiting professor Ben Fry.
[For more graphs of interest, expand this article… ]
edit: oh and this is cool too: Bipartite graphs between CEO’s and the corporations they’ve worked at. http://www.theyrule.net/
VisualComplexity [link
] showcases many graphs from different fields.
Here are some:
Influence between Writers/Artists
* You can follow any responses to this entry through the RSS 2.0 feed.