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:
- Introduction of a new document into the existing collection reduces the PageRank value of existing documents
- 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.
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