How a Page Rank is calculated in Gephi

This blog will illustrate how a Page Rank is calculated in Gephi and how it is used in social network analysis. The blog includes a video which explains the concept in detail:

The Page Rank concept is a way in which a web page or social network node can be given an “importance score”. This importance score will always be a non-negative real number and all the scores (in the network) will add to 1, sometimes it might be expressed as a percentage. Before beginning the calculation, you must remove the self-loops, otherwise, the Page Rank will not sum up to 1. You can do this by filtering out the self-loops (see figure 1 and the video for details).

Self Loops

Figure 1: Filtering self-loops.

The Page Rank score for a given page/node is based on the links made to that said page/node from other pages/nodes. The links to a given page/node are called the backlinks/in-degrees for that page/node. The web/social network thus becomes a democracy where pages/nodes vote for the importance of other pages by linking to them. It is a variant of the Eigenvector value, but because it uses backlinks/in-degrees it is used in directed networks. Directed networks are networks that allow handles (the node or webpage) to follow another without that page or node following back.

The formula for the Page Rank score is illustrated in figure 2:

Page Rank Formula

Figure 2: Page Rank Formula

The objective is to develop a set of simultaneous equations to solve for each Page Rank. The formula also needs a damping factor (or probability as stated in Gephi). For each node, identify the other nodes linking to it. These “other nodes” will give the “targeted node” a proportion of their out-going links. A simple example is illustrated in Figure 3a, 3b and 3c:

Figure 3a: Page rank

Figure 3a: Page rank Calculation


Page Rank

Figure 3b: Page Rank Calculation


Page Rank Calculation

Figure 3c: Page Rank Calculation

The reality of calculating the Page Rank of any webpage or social network analysis is, the links will be very large. So, doing the calculations by hand become almost impossible. Platforms will Gephi have the algorithms built-in so the processing can be quick. It is what I use when doing such a calculation. Hopefully, though, you now understand the principles of the calculation.

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Dr Alan Shaw is a Senior Lecturer and Marketing consultant focusing on a range of sectors. His main interests are in strategy development, social marketing, digital marketing, advertising, consumer behaviour and marketing application.
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