# Weighted PageRank

The only difference between weighted PageRank and standard PageRank is that edges have weights, and the influence that a vertex receives from an in-neighbor is multiplied by the weight of the in-edge.

## Specifications

``````tg_pageRank_wt (SET<STRING> v_type, SET<STRING> e_type, STRING wt_attr,
FLOAT max_change=0.001, INT max_iter=25, FLOAT damping=0.85, INT top_k=100,
BOOL print_accum = TRUE, STRING result_attr =  "", STRING file_path = "",
BOOL display_edges = FALSE)``````

### Time complexity

This algorithm has a time complexity of O(E*k) where E is the number of edges and k is the number of iterations.

The number of iterations is data-dependent, but the user can set a maximum. Parallel processing reduces the time needed for computation.

Characteristic Value

Result

Computes a weighted PageRank value (FLOAT type) for each vertex.

Input Parameters

• `STRING v_type`: Names of vertex type to use

• `STRING e_type`: Names of edge type to use

• `STRING wt_attr`: Name of edge weight attribute

• `FLOAT max_change`: PageRank will stop iterating when the largest difference between any vertex’s current score and its previous score ≤ `max_change`. That is, the scores have become very stable and are changing by less than `max_change` from one iteration to the next.

• `INT max_iter`: Maximum number of iterations.

• `FLOAT damping`: Fraction of score that is due to the score of neighbors. The balance (1 - damping) is a minimum baseline score that every vertex receives.

• `INT top_k`: Sort the scores highest first and output only this many scores

• `BOOL print_accum`: If True, output JSON to standard output

• `STRING result_attr`: If not empty, store PageRank values (FLOAT) to this attribute

• `STRING file_path`: If not empty, write output to this file.

• `BOOL display_edges`: If true, include the graph’s edges in the JSON output, so that the full graph can be displayed.

Result Size

V = number of vertices

Graph Types

Directed edges