Background
Inter-domain Routing and the Border Gateway Protocol
There is an abundance of literature on BGP and Inter-domain routing. Listed below are some useful references for starters to BGP.

1. Cisco's BGP Documentation

2. Border Gateway Protocol 4, RFC 1771

3. IRL's Internet Topology Project, contains the most updated AS level topology of the Internet.
 
The LinkRank Concept
What is a LinkRank (LR) graph?
LinkRank graphs weigh the links between autonomous systems by the number of routing prefixes going through each link for each monitoring session. Each monitoring session may have different LinkRank graphs. Each LinkRank graph indicates the popularity of links from the view of the monitoring session. In our client, we do not provide separate LinkRank graphs, but instead include the LinkRank weight in the Rank-Change graphs explained below.
What is a Rank-Change (RC) graph?
Rank-Change graphs are constructed by tracing LinkRank graphs over time and associating the weight of edges with the difference in the weights of the individual links. A negative weight indicates routes lost on a link, while positive weight indicates routes gained in that time period. The LinkRank client displays only the Rank-Change graphs, but with an option of link weights showing absolute LinkRank values.The LinkRank client displays only the Rank-Change graphs, but with an option of link weights showing absolute LinkRank values. Figure shows the Rank-Change graph from the perspective of a router in AS 7018. In the time interval considered, the link between AS 7018 and AS 3320 lost 53 routes (red line), and these shifted to other links via AS 5511 (green lines). For each link shown, the first value is the LinkRank indicating the number of routes which use that link (e.g. 0 for link between AS 9163 and AS 8390) and the figure in bracket indicates the change in ranks (e.g. 53 routes lost on link between AS 9163 and AS 8390). Note, all weights are as viewed from the router in AS 7018 (blue node), and the same links could have different weights as observed from other observation points.

Based on this graph, users of LinkRank can attempt to understand which part of the network caused these routing changes.
How are activity snapshots plotted?
Activity snapshots is an integral part of the LinkRank tool and helps in identifying periods of routing dynamics. Activity snapshots summarize the rank changes in terms of red/green bars with red indicating links losing routes and green indicating links gaining routes. In the example below, the total gain in the time interval is 200, while the total loss is 100. Such an activity summary is created for each time entry of Rank-Change values and plotted on a time scale. Thus looking at an activity graph, one can get an idea of amount of routing activity as well as identify specific times of high or unusual activity.
 
References
Inferring the Origin of Routing Changes using Link Weights
Mohit Lad, Ricardo Oliveira, Dan Massey and Lixia Zhang, IEEE International Conference on Network Protocols (ICNP), October 2007.
[PDF]
Visualizing Internet Routing Changes
Mohit Lad, Dan Massey and Lixia Zhang, IEEE Transactions on Visualization and Computer Graphics, special issue on Visual Analytics, November/December 2006.
[PDF]
Using Link-Rank for BGP Visualization
Mohit Lad, Yiguo Wu, Dan Massey and Lixia Zhang, talk given at Nanog-34, BOF session, May 2005.
[Talk Slides]
LinkRank: A Graphical Tool for Capturing BGP Routing Dynamics
Mohit Lad, Dan Massey and Lixia Zhang, in Proceedings of The IEEE/IPIF Network Operations and Management Symposium (NOMS), April 2004.
[PDF]
[Talk Slides in quicktime]
LinkRank: A Tool for Visualizing BGP Dynamics
Mohit Lad, Timothy Ma, Dan Massey and Lixia Zhang, talk given at Nanog-32, Reston, Virginia , October 2004.
[Abstract and slides]