# Updating pagerank with iterative aggregation

Mathematical Page Ranks for a simple network, expressed as percentages.

(Google uses a logarithmic scale.) Page C has a higher Page Rank than Page E, even though there are fewer links to C; the one link to C comes from an important page and hence is of high value.  Similarly, edges have corresponding source and destination vertex identifiers.

I'm looking for a proof of the algorithm's convergence, and I'm also looking for a proof that the convergence limit is unique. Hi, dvd03-ga: Is A (in the "power method") the same as D in the previous definition?

Assuming convergence, the uniqueness of any bounded limit (independent of the starting value) can be related to the properties of A easily, as the limit r must by continuity satisfy the equation: r = (1-c)*u r*A r*(I-A) = (1-c)*u and the limit is unique provided (I-A) is invertible.

To support graph computation, Graph X exposes a set of fundamental operators (e.g., subgraph, join Vertices, and aggregate Messages) as well as an optimized variant of the Pregel API.

In addition, Graph X includes a growing collection of graph algorithms and builders to simplify graph analytics tasks.

r_ - r_n