PageRank
The PageRank algorithm ranks the nodes in a graph by their relative importance or influence. PageRank determines each node's ranking by identifying the number of links to the node and the quality of the links. The quality of a link is determined by the importance (PageRank) of the node that presents the outbound link.
PageRank Syntax
Graph algorithms are accessed from an internal SPARQL service endpoint. To incorporate the PageRank algorithm in a query, include a SERVICE statement in the WHERE clause. The service call specifies the name of the algorithm and defines the required and optional property values for that algorithm.
Use the following syntax to compute the PageRank for nodes in a graph. The table below describes each property.
SERVICE <csi:page_rank> {
[] <csi:binding-vertex> ?vertex_variable_name ;
<csi:binding-rank> ?rank_variable_name ;
<csi:edge-label> <edge_uri> ;
[ <csi:graph> <graph_uri> ; ]
[ <csi:max-iterations> number_of_iterations ; ]
[ <csi:err-tolerance> tolerance_number ; ]
[ <csi:damping-factor> double_value ; ]
[ <csi:normalized> boolean_value ]
}
| Property | Description | Range & Default Value |
|---|---|---|
| <csi:binding-vertex> | Required property that defines the name to use for the column in the results that lists the source nodes or vertices. | Range: Must be a variable name Default: none |
| <csi:binding-rank> | Required property that defines the name to use for the result column that lists the computed PageRank values. | Range: Must be a variable name Default: none |
| <csi:edge-label> | Required property that lists the edge URI that defines the graph to operate on. The graph is the set of vertices that are connected by this URI. | Range: Must be a URI Default: none |
| <csi:graph> | Optional property that specifies the graph to query. | Range: Must be a URI Default: none |
| <csi:max-iterations> | Optional property that specifies the maximum number of times to iterate through the graph to adjust approximate PageRank values. | Range: 1 - 100 Default: 50 |
| <csi:err-tolerance> | Optional property that specifies the error tolerance to use. If the sum of the error values for all nodes is below this tolerance value, AnzoGraph stops PageRank iterations. | Range: 0.0 - 0.1 Default: 1e-8 |
| <csi:damping-factor> | Optional property that specifies the edge traversal probability. When used for analyzing website data, such as when Google ranks search results, the damping factor represents click-through probability. The damping-factor value is subtracted from 1.0 in the calculation. | Range: 0.0 - 1.0 Default: 0.85 |
| <csi:normalized> | Optional property that specifies whether to produce PageRank values that are between 0 and 1. | Range: true or false Default: false |
PageRank Examples
The examples below are run against a sample flight network data set, which contains data about flights, airlines, and airport locations. For instructions on downloading the sample data and loading it to AnzoGraph so that you can run the example queries, see Sample Data for Graph Algorithm Examples.
The example below uses the PageRank algorithm to find the 10 most connected airports. The edge to operate on is defined as the hasRouteTo URI, which links the airport nodes.
prefix : <http://anzograph.com/data#>
prefix fl: <http://anzograph.com/flights/>
prefix owl: <http://www.w3.org/2002/07/owl#>
prefix skos: <http://www.w3.org/2004/02/skos/core#>
SELECT ?airport ?rank
FROM <http://anzograph.com/airline_flight_network>
WHERE
{
?node a fl:Airport .
?node skos:prefLabel ?airport .
SERVICE <csi:page_rank>
{
[] <csi:binding-vertex> ?node ;
<csi:binding-rank> ?rank ;
<csi:edge-label> <http://anzograph.com/flights/hasRouteTo> .
}
}
ORDER BY desc(?rank)
LIMIT 10
The results show that Chicago O'Hare has the highest PageRank. It has the highest number of links to other airports.
airport | rank ---------------------------------------------------+----------- Chicago O'Hare International Airport | 13.412187 Dallas Fort Worth International Airport | 13.163151 Hartsfield Jackson Atlanta International Airport | 12.807295 Denver International Airport | 10.381292 George Bush Intercontinental Houston Airport | 8.381458 Salt Lake City International Airport | 6.901801 Minneapolis-St Paul International/Wold-Chamberlain | 6.243941 San Francisco International Airport | 5.507264 Phoenix Sky Harbor International Airport | 5.274814 Los Angeles International Airport | 5.245441 10 rows