PageRank Modelling Study

This is an academic study of controlled PageRank modelling of a simplified link graph in a collection of three documents.

Key Observations:

  1. Introduction of a new document into the existing collection reduces the PageRank value of existing documents
  2. Differences in PageRank value of chain-linked documents vs. directly linked documents

Experiment Parameters:

  • Graph Type: Directed
  • Epsilon: 0.2 (default: 0.001)
  • Probability: 0.85
  • Use edge weight: Yes


  • ‘Node’ = page.
  • ‘Edge’ = link, can have two directions and three states (a->b, b->a and a<->b)
  • ‘Link Graph’ = collection of nodes and edges

The Test

Using the traditional formula we calculate the distribution of PageRank between two nodes connected with an a->b edge resulting in the initial PageRank split of:
  • Node a: 0.33
  • Node b: 0.66.


Introduction of a completely new node in existing the collection (in our case the three nodes and one directed edge represent the entire web). Observe the change in PageRank allocation.

  • Node a: 0.27 (old value 0.33)
  • Node b: 0.47 (old value: 0.66)
  • Node c: 0.27 (new node)


An edge between Node c and Node a will pass fraction of the Node c PageRank which will in turn pass the extra value to Node b.

The outcome:

  • Node a: 0.35 (old 0.27)
  • Node b: 0.45 (old 0.47)
  • Node c: 0.2 (old 0.27)



PageRank modelling for the purposes of this study was calculated using Gephi.

Dan Petrovic, the managing director of DEJAN, is Australia’s best-known name in the field of search engine optimisation. Dan is a web author, innovator and a highly regarded search industry event speaker.

More Posts - Website