Supported Graph Characteristics

Unweighted edges

Directed edges

Undirected edges

Homogeneous vertex types

Algorithm links: PageRank

The PageRank algorithm measures the influence of each vertex on every other vertex. PageRank influence is defined recursively: a vertex’s influence is based on the influence of the vertices which refer to it. A vertex’s influence tends to increase if either of these conditions are met:

  1. It has more referring vertices

  2. Its referring vertices have higher influence

The analogy to social influence is clear.

A common way of interpreting PageRank value is through the Random Network Surfer model. A vertex’s PageRank score is proportional to the probability that a random network surfer will be at that vertex at any given time. A vertex with a high PageRank score is a vertex that is frequently visited, assuming that vertices are visited according to the following Random Surfer scheme:

  • Assume a person travels or surfs across a network’s structure, moving from vertex to vertex.

  • The surfer can start anywhere. This start-anywhere property is part of the magic of PageRank, meaning the score is a truly fundamental property of the graph structure itself.

  • Each round, the surfer randomly picks one of the outward connections from the surfer’s current location. The surfer repeats this random walk for a long time.

  • There is a small probability that the surfer’s next step will be a random vertex instead of a connected vertex. This probability is expressed in the algorithm as (1 - damping).


For more information, see the Google paper on PageRank.


tg_pagerank (STRING v_type, STRING e_type,  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)


Parameter Description Default

STRING v_type

Names of vertex type to use

(empty string)

STRING e_type

Names of edge type to use

(empty string)

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 in FLOAT format to this vertex attribute

(empty string)

STRING file_path

If not empty, write output to this file.

(empty string)

BOOL display_edges

If true, include the graph’s edges in the JSON output, so that the full graph can be displayed.



Computes a PageRank FLOAT value for each vertex and stores it in a specified attribute on each vertex.

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.


 # Use _ for default values
RUN QUERY tg_pagerank("Person", "Friend", 0.001, 25, 0.85, 100 _, _, _, _)

We ran PageRank on our test10 graph (using Friend edges) with the following parameter values:

  • damping=0.85

  • max_change=0.001

  • max_iter=25

We see that Ivy (center bottom) has the highest PageRank score (1.12). This makes sense since there are 3 neighboring persons who point to Ivy, more than for any other person. Ivy’s high PageRank score indicates that Ivy is a relatively important person in this social group.

Eddie and Justin have scores of exactly 1 because they do not have any out-edges. This is an artifact of our particular version of PageRank. Likewise, Alex has a score of 0.15. This comes from (1 - damping), because Alex has no in-edges, meaning that Alex could only have been reached by a random visit rather than a directed connection.

Visualized results of example query on social10 graph