# The Sensitivity of Page Rank to Connection Errors

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Large networks taken from the social sciences often contain "connection errors" in which the edges are mistakenly recorded. For example, an set of extra edges can be wrongly added, a set of edges can be wrongly deleted, or a set of edges may be "transposed", that is, an edge that should be recorded as going from node A to node B is transposed and falsely recorded as going from node A to node C. This Demonstration examines the sensitivity of the page rank measure of node centrality to these "connection errors" in a random graph. You choose the number of nodes and edges in the original random graph. By moving the "variant" slider you then choose an example of a random graph satisfying these criteria for the original random graph. You then choose how many random edges to add, delete, or transpose from the graph using the "operation" control in conjunction with the "error parameter" slider. That slider responds in either a linear or logarithmic fashion depending on the "transposition fraction mode" you have selected. By triggering the "perturb" control, the Demonstration generates sets of errors satisfying the constraints established by the prior controls.

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Contributed by: Seth J. Chandler (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The Demonstration makes use of an ordering metric for each node, which is the difference between the order of the page rank of that node in the original graph and the order of the page rank of that node in the original graph with edges deleted. Thus, an absolute mean of 2.6 in a graph with 10 nodes means that on average a node changes 2.6 places in the page rank ordering as a result of the deletion of nodes.

## Permanent Citation

"The Sensitivity of Page Rank to Connection Errors"

http://demonstrations.wolfram.com/TheSensitivityOfPageRankToConnectionErrors/

Wolfram Demonstrations Project

Published: March 7 2011