Consider weighting edges based on the difference in degree between their nodes. (an edge from a high-degree node to a low degree node is unlikely to be important.
Consider weighting nodes based on their degree. (The higher the degree of a node, the less likely it is to be important to the context.)
This may not jive with how pagerank works. High degree nodes may tell you a lot about the topic, just not nodes you reach through them.
Consider weighting edges based on the difference in degree between their nodes. (an edge from a high-degree node to a low degree node is unlikely to be important.
Consider weighting nodes based on their degree. (The higher the degree of a node, the less likely it is to be important to the context.)