# 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

## Definitions:

• ‘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

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.