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I have a graph that over time new nodes can be added to it and new links between nodes can be added. at any given time t, I create a network using all nodes and edges up to time t and calculate the page rank of each node. For time t+1, I take all the nodes and edges up to time t+1 (so this network includes all the nodes and edges in the graph that was made at time t and possibly some new nodes and edges) and then calculate the page rank of the nodes again. Now let's say the PageRank of node n1 at time t is x1, and the PageRank of the same node n1 at time t+1 is x2. What is an appropriate way to compare x1 and x2 given that they have been obtained from two different graphs? I would like to be able to say if the PageRank of a node has increased or decreased over time.

Consider a scenario in which a node has scored .6 in a network made at time t and the majority of other nodes scored .1 or less. The same node scores .6 in a network made at time t+1 but now the majority of other nodes score closer to .01. Is it fair to say this node's centrality rank(pagerank) has stayed the same given that the network t and network t+1 are so different?

Mina
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I would like to be able to say if the PageRank of a node has increased or decreased over time.

"The ( PageRank ) score of each node is the probability of the random surfer to be at this node at some point in time.

The probability should be a mumber between 0 and 1 ( or perhaps between 0 and 100% ) - in any case, a number. So if the new number is larger than the old, then the PageRank has increased.

In your scenario the relative rank has increased, but the absolute rank has remained the same.

ravenspoint
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