Common Neighbour Aware Random Walk sampling
This feature is in the beta tier. For more information on feature tiers, see API Tiers.
Glossary
 Directed

Directed trait. The algorithm is welldefined on a directed graph.
 Directed

Directed trait. The algorithm ignores the direction of the graph.
 Directed

Directed trait. The algorithm does not run on a directed graph.
 Undirected

Undirected trait. The algorithm is welldefined on an undirected graph.
 Undirected

Undirected trait. The algorithm ignores the undirectedness of the graph.
 Heterogeneous nodes

Heterogeneous nodes fully supported. The algorithm has the ability to distinguish between nodes of different types.
 Heterogeneous nodes

Heterogeneous nodes allowed. The algorithm treats all selected nodes similarly regardless of their label.
 Heterogeneous relationships

Heterogeneous relationships fully supported. The algorithm has the ability to distinguish between relationships of different types.
 Heterogeneous relationships

Heterogeneous relationships allowed. The algorithm treats all selected relationships similarly regardless of their type.
 Weighted relationships

Weighted trait. The algorithm supports a relationship property to be used as weight, specified via the relationshipWeightProperty configuration parameter.
 Weighted relationships

Weighted trait. The algorithm treats each relationship as equally important, discarding the value of any relationship weight.
1. Introduction
Graph sampling algorithms are used to reduce the complexity of large and complex graphs while preserving their essential properties. They can help to speed up computation, reduce bias, and ensure privacy, making graph analysis more manageable and accurate. They are widely used in network analysis, machine learning, and social network analysis, among other applications.
The Common Neighbour Aware Random Walk (CNARW) is a graph sampling technique that involves optimizing the selection of the nexthop node. It takes into account the number of common neighbours between the current node and the nexthop candidates.
According to the paper, a major reason why simple random walks tend to converge slowly is due to the high clustering feature that is typical for some kinds of graphs e.g. for online social networks (OSNs). When moving to neighbours uniformly at random, it is easy to get caught in local loops and revisit previously visited nodes, which slows down convergence.
To address this issue, one solution is to prioritize nodes that offer a higher likelihood of exploring unvisited nodes in each step. Nodes with higher degrees may provide this opportunity, but they may also have more common neighbours with previously visited nodes, increasing the likelihood of revisits.
Therefore, choosing a node with a higher degree and fewer common neighbours with previously visited nodes (or the current node) not only increases the chances of discovering unvisited nodes but also reduces the probability of revisiting previously visited nodes in future steps.
The implementation of the algorithm is based on the following paper:
1.1. Relationship weights
Same as in the relationshipWeightProperty
parameter in RandomWalksWithRestarts
algorithm.
1.2. Node label stratification
Same as in the nodeLabelStratification
parameter in RandomWalksWithRestarts
algorithm.
2. Syntax
CALL gds.graph.sample.cnarw(
graphName: String,
fromGraphName: String,
configuration: Map
)
YIELD
graphName,
fromGraphName,
nodeCount,
relationshipCount,
startNodeCount,
projectMillis
Name  Type  Description 

graphName 
String 
The name of the new graph that is stored in the graph catalog. 
fromGraphName 
String 
The name of the original graph in the graph catalog. 
configuration 
Map 
Additional parameters to configure the subgraph sampling. 
Name  Type  Default  Optional  Description 

List of String 

yes 
Filter the named graph using the given node labels. 

List of String 

yes 
Filter the named graph using the given relationship types. 

Integer 

yes 
The number of concurrent threads used for running the algorithm. 

String 

yes 
An ID that can be provided to more easily track the algorithm’s progress. 

Boolean 

yes 
If disabled the progress percentage will not be logged. 

String 

yes 
Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted. 

samplingRatio 
Float 

yes 
The fraction of nodes in the original graph to be sampled. 
restartProbability 
Float 

yes 
The probability that a sampling random walk restarts from one of the start nodes. 
startNodes 
List of Integer 

yes 
IDs of the initial set of nodes of the original graph from which the sampling random walks will start. 
nodeLabelStratification 
Boolean 

yes 
If true, preserves the node label distribution of the original graph. 
randomSeed 
Integer 

yes 
The seed value to control the randomness of the algorithm.
Note that 
Name  Type  Description 

graphName 
String 
The name of the new graph that is stored in the graph catalog. 
fromGraphName 
String 
The name of the original graph in the graph catalog. 
nodeCount 
Integer 
Number of nodes in the subgraph. 
relationshipCount 
Integer 
Number of relationships in the subgraph. 
startNodeCount 
Integer 
Number of start nodes actually used by the algorithm. 
projectMillis 
Integer 
Milliseconds for projecting the subgraph. 
3. Examples
In this section we will demonstrate the usage of the CNARW sampling algorithm on a small toy graph.
3.1. Setting up
In this section we will show examples of running the Common Neighbour Aware Random Walk graph sampling algorithm on a concrete graph. The intention is to illustrate what the results look like and to provide a guide in how to make use of the algorithm in a real setting. We will do this on a small social network graph of a handful nodes connected in a particular pattern. The example graph looks like this:
CREATE
(J:female {id:'Juliette'}),
(R:male {id:'Romeo'}),
(r1:male {id:'Ryan'}),
(r2:male {id:'Robert'}),
(r3:male {id:'Riley'}),
(r4:female {id:'Ruby'}),
(j1:female {id:'Josie'}),
(j2:male {id:'Joseph'}),
(j3:female {id:'Jasmine'}),
(j4:female {id:'June'}),
(J)[:LINK]>(R),
(R)[:LINK]>(J),
(r1)[:LINK]>(R), (R)[:LINK]>(r1),
(r2)[:LINK]>(R), (R)[:LINK]>(r2),
(r3)[:LINK]>(R), (R)[:LINK]>(r3),
(r4)[:LINK]>(R), (R)[:LINK]>(r4),
(r1)[:LINK]>(r2), (r2)[:LINK]>(r1),
(r1)[:LINK]>(r3), (r3)[:LINK]>(r1),
(r1)[:LINK]>(r4), (r4)[:LINK]>(r1),
(r2)[:LINK]>(r3), (r3)[:LINK]>(r2),
(r2)[:LINK]>(r4), (r4)[:LINK]>(r2),
(r3)[:LINK]>(r4), (r4)[:LINK]>(r3),
(j1)[:LINK]>(J), (J)[:LINK]>(j1),
(j2)[:LINK]>(J), (J)[:LINK]>(j2),
(j3)[:LINK]>(J), (J)[:LINK]>(j3),
(j4)[:LINK]>(J), (J)[:LINK]>(j4),
(j1)[:LINK]>(j2), (j2)[:LINK]>(j1),
(j1)[:LINK]>(j3), (j3)[:LINK]>(j1),
(j1)[:LINK]>(j4), (j4)[:LINK]>(j1),
(j2)[:LINK]>(j3), (j3)[:LINK]>(j2),
(j2)[:LINK]>(j4), (j4)[:LINK]>(j2),
(j3)[:LINK]>(j4), (j4)[:LINK]>(j3) ;
This graph has two clusters of Users, that are closely connected. Between those clusters there is bidirectional relationship.
We can now project the graph and store it in the graph catalog.
In the examples below we will use named graphs and native projections as the norm. However, Cypher projections can also be used. 
CALL gds.graph.project( 'myGraph', ['male', 'female'], 'LINK' );
3.2. Sampling
We can now go on to sample a subgraph from "myGraph" using CNARW. Using the "Juliette" node as our set of start nodes, we will venture to visit five nodes in the graph for our sample. Since we have six nodes total in our graph, and 5/10 = 0.5 we will use this as our sampling ratio.
MATCH (start:female {id: 'Juliette'})
CALL gds.graph.sample.cnarw('mySampleCNARW', 'myGraph',
{
samplingRatio: 0.5,
startNodes: [id(start)]
})
YIELD nodeCount
RETURN nodeCount;
nodeCount 

5 
Due to the random nature of the sampling the algorithm may return different counts in different runs.
The main difference between the Common Neighbour Aware Random Walk and Random Walks with Restarts graphs sampling algorithms is that there are more chances to go into another cluster for the first one, which is colored in blue in the example above. The relationships sampled are those connecting these nodes.
3.3. Memory Estimation
First off, we will estimate the cost of running the algorithm using the estimate
procedure.
This can be done with any execution mode.
Estimating the sampling procedure is useful to understand the memory impact that running the procedure on your graph will have.
If the estimation shows that there is a very high probability of the execution going over its memory limitations, the execution is prohibited.
To read more about this, see Automatic estimation and execution blocking.
For more details on estimate
in general, see Memory Estimation.
CALL gds.graph.sample.cnarw.estimate('myGraph',
{
samplingRatio: 0.5
})
YIELD requiredMemory
RETURN requiredMemory;
requiredMemory 

"1264 Bytes" 
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