Prestige Plugin

Gephi Prestige Metrics

This plugin can calculate the following four prestige metrics on DIRECTED Graphs.

Indegree Prestige

The Indegree Prestige metric for a node v is defined by the number of other nodes that are directly pointing to v. As a result there are two additional node properties created:

• pr_indegree: Indegree prestige of v
• pr_indegree_normalized : Normalized Indegree prestige, which is calculated by dividing "Indegree Prestige" by (Number of nodes -1). This value will always between 0 and 1 (0 = no other nodes are directly pointing to v, wherease 1 means that all other nodes are directly pointing to v)

Domain Prestige

The Domain Prestige metric for a node v is the fraction of nodes within a network that are directly od indirectly pointing to v. This answers the question: Which fraction of the network can reach node v. The Result is stored in the node property pr_domain

Proximity Prestige

The Proximity Prestige can be seen as an extension of the Indegree Prestige. Indegree Prestige is a local measurement because only directly connected nodes are counted. Proximity prestige for a node v also considers nodes that are indirectly pointing to v. The path lengths are used for weighting; shorter paths are more valuable.

The formula is:

Paremeters:

v: Node for which the Proximity Prestige is calculated

I: Set of nodes which are directly or indirectly pointing to v

Sum(d): Sum of all shortest paths from all Nodes in I to v

above = Fraction of Nodes pointing (directly or indirectly) to v = |I| / (n-1)

below = Average shortest path lengths of Nodes pointing to v: SUM(d) / |I|

ProxiityPrestige (v) = above / below

The result is stored in the node attribute pr_proximity.

Rank Prestige

The Rank Prestige is similar to the Indegree Prestige. But instead of just counting the number of connected nodes the rank / status / prominence of the neighbour nodes is considered and must be defined. Therefore the setup is a bit more complicated. You have to select a nummeric or boolean attribute called prominence, which indicates the status of a person (e.g. Number of fans). To calculate the Rank Prestige of a node v, all the prominence values from nodes directly pointing to v are summed up.

There is an option to log-transform the result.

Finally two node attributes are created:

• pr_rank: Rank-Value for node
• pr_rank_min-max-normalized: Min-Max-Normalized Rank-Value for node