CELF

Glossary

Directed: Directed trait. The algorithm is well-defined 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 well-defined 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.

Introduction

The influence maximization problem asks for a set of k nodes that maximize the expected spread of influence in the network. The set of these initial k is called the seed set.

The Neo4j GDS Library supports approximate computation of the best seed set under the Independent Cascade propagation model. In this propagation model, initially we assume that the nodes in the seed set become influenced and the process works as follows. An influenced node influences each of its neighbors with probability p. The spread is then the number of nodes that become influenced.

The Neo4j GDS Library supports the CELF algorithm, introduced in 2007 by Leskovec et al. in Cost-effective Outbreak Detection in Networks to compute a seed set with a large expected spread.

The CELF algorithm is based on the Greedy algorithm for the problem. It works iteratively in k steps to create the returned seed set S, where at each step the node yielding the maximum expected spread gain is added to S.

The expected spread gain of a node u not in S is estimated by running mc different Monte Carlo simulations of the propagation process and counting for each simulation the number of nodes that would become influenced if u were to be added in S.

The CELF algorithm extends on Greedy by introducing a lazy forwarding mechanism, which prunes a lot of nodes from being examined, thereby massively reducing the number of conducted simulations. This makes CELF much faster than Greedy on large networks.

Syntax

CELF syntax per mode

Run CELF in stream mode on a named graph.

CALL gds.influenceMaximization.celf.stream(
  graphName: String,
  configuration: Map
)
YIELD
  nodeId: Integer,
  spread: Float

Table 1. Parameters
Name	Type	Default	Optional	Description
graphName	String	`n/a`	no	The name of a graph stored in the catalog.
configuration	Map	`{}`	yes	Configuration for algorithm-specifics and/or graph filtering.

Table 2. Configuration
Name	Type	Default	Optional	Description
nodeLabels	List of String	`['*']`	yes	Filter the named graph using the given node labels. Nodes with any of the given labels will be included.
relationshipTypes	List of String	`['*']`	yes	Filter the named graph using the given relationship types. Relationships with any of the given types will be included.
concurrency	Integer	`4`	yes	The number of concurrent threads used for running the algorithm.
jobId	String	`Generated internally`	yes	An ID that can be provided to more easily track the algorithm’s progress.
logProgress	Boolean	`true`	yes	If disabled the progress percentage will not be logged.
seedSetSize	Integer	`n/a`	no	The number of nodes that maximize the expected spread in the network.
monteCarloSimulations	Integer	`100`	yes	The number of Monte-Carlo simulations.
propagationProbability	Float	`0.1`	yes	The probability of a node being activated by an active neighbour node.
randomSeed	Integer	`n/a`	yes	The seed value to control the randomness of the algorithm.

Table 3. Results
Name	Type	Description
nodeId	Integer	Node ID.
spread	Float	The spread gained by selecting the node.

Run CELF in stats mode on a named graph.

CALL gds.influenceMaximization.celf.stats(
  graphName: String,
  configuration: Map
)
YIELD
  computeMillis: Integer,
  totalSpread: Float,
  nodeCount: Integer,
  configuration: Map

Table 4. Parameters
Name	Type	Default	Optional	Description
graphName	String	`n/a`	no	The name of a graph stored in the catalog.
configuration	Map	`{}`	yes	Configuration for algorithm-specifics and/or graph filtering.

Table 5. Configuration
Name	Type	Default	Optional	Description
nodeLabels	List of String	`['*']`	yes	Filter the named graph using the given node labels. Nodes with any of the given labels will be included.
relationshipTypes	List of String	`['*']`	yes	Filter the named graph using the given relationship types. Relationships with any of the given types will be included.
concurrency	Integer	`4`	yes	The number of concurrent threads used for running the algorithm.
jobId	String	`Generated internally`	yes	An ID that can be provided to more easily track the algorithm’s progress.
logProgress	Boolean	`true`	yes	If disabled the progress percentage will not be logged.
seedSetSize	Integer	`n/a`	no	The number of nodes that maximize the expected spread in the network.
monteCarloSimulations	Integer	`100`	yes	The number of Monte-Carlo simulations.
propagationProbability	Float	`0.1`	yes	The probability of a node being activated by an active neighbour node.
randomSeed	Integer	`n/a`	yes	The seed value to control the randomness of the algorithm.

Table 6. Results
Name	Type	Description
computeMillis	Integer	Milliseconds for running the algorithm.
totalSpread	Float	The sum of individual seed set node spreads.
nodeCount	Integer	Number of nodes in the graph.
configuration	Map	The configuration used for running the algorithm.

Run CELF in mutate mode on a named graph.

CALL gds.influenceMaximization.celf.mutate(
  graphName: String,
  configuration: Map
)
YIELD
  mutateMillis: Integer,
  nodePropertiesWritten: Integer,
  computeMillis: Integer,
  totalSpread: Float,
  nodeCount: Integer,
  configuration: Map

Table 7. Parameters
Name	Type	Default	Optional	Description
graphName	String	`n/a`	no	The name of a graph stored in the catalog.
configuration	Map	`{}`	yes	Configuration for algorithm-specifics and/or graph filtering.

Table 8. Configuration
Name	Type	Default	Optional	Description
nodeLabels	List of String	`['*']`	yes	Filter the named graph using the given node labels.
relationshipTypes	List of String	`['*']`	yes	Filter the named graph using the given relationship types.
concurrency	Integer	`4`	yes	The number of concurrent threads used for running the algorithm.
jobId	String	`Generated internally`	yes	An ID that can be provided to more easily track the algorithm’s progress.
seedSetSize	Integer	`n/a`	no	The number of nodes that maximize the expected spread in the network.
monteCarloSimulations	Integer	`100`	yes	The number of Monte-Carlo simulations.
propagationProbability	Float	`0.1`	yes	The probability of a node being activated by an active neighbour node.
randomSeed	Integer	`n/a`	yes	The seed value to control the randomness of the algorithm.

Table 9. Results
Name	Type	Description
mutateMillis	Integer	Milliseconds for adding properties to the projected graph.
nodePropertiesWritten	Integer	Number of properties added to the projected graph.
computeMillis	Integer	Milliseconds for running the algorithm.
totalSpread	Float	The sum of individual seed set node spreads.
nodeCount	Integer	Number of nodes in the graph.
configuration	Map	The configuration used for running the algorithm.

Run CELF in write mode on a named graph.

CALL gds.influenceMaximization.celf.write(
  graphName: String,
  configuration: Map
)
YIELD
  writeMillis: Integer,
  nodePropertiesWritten: Integer,
  computeMillis: Integer,
  totalSpread: Float,
  nodeCount: Integer,
  configuration: Map

Table 10. Parameters
Name	Type	Default	Optional	Description
graphName	String	`n/a`	no	The name of a graph stored in the catalog.
configuration	Map	`{}`	yes	Configuration for algorithm-specifics and/or graph filtering.

Table 11. Configuration
Name	Type	Default	Optional	Description
nodeLabels	List of String	`['*']`	yes	Filter the named graph using the given node labels. Nodes with any of the given labels will be included.
relationshipTypes	List of String	`['*']`	yes	Filter the named graph using the given relationship types. Relationships with any of the given types will be included.
concurrency	Integer	`4`	yes	The number of concurrent threads used for running the algorithm.
jobId	String	`Generated internally`	yes	An ID that can be provided to more easily track the algorithm’s progress.
logProgress	Boolean	`true`	yes	If disabled the progress percentage will not be logged.
writeConcurrency	Integer	`value of 'concurrency'`	yes	The number of concurrent threads used for writing the result to Neo4j.
seedSetSize	Integer	`n/a`	no	The number of nodes that maximize the expected spread in the network.
monteCarloSimulations	Integer	`100`	yes	The number of Monte-Carlo simulations.
propagationProbability	Float	`0.1`	yes	The probability of a node being activated by an active neighbour node.
randomSeed	Integer	`n/a`	yes	The seed value to control the randomness of the algorithm.

Table 12. Results
Name	Type	Description
writeMillis	Integer	Milliseconds for adding properties to the projected graph.
nodePropertiesWritten	Integer	Number of properties added to the Neo4j database.
computeMillis	Integer	Milliseconds for running the algorithm.
totalSpread	Float	The sum of individual seed set node spreads.
nodeCount	Integer	Number of nodes in the graph.
configuration	Map	The configuration used for running the algorithm.

Examples

All the examples below should be run in an empty database.

The examples use Cypher projections as the norm. Native projections will be deprecated in a future release.

In this section we will show examples of running the CELF 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:

The following Cypher statement will create the example graph in the Neo4j database:

CREATE
  (a:Person {name: 'Jimmy'}),
  (b:Person {name: 'Jack'}),
  (c:Person {name: 'Alice'}),
  (d:Person {name: 'Ceri'}),
  (e:Person {name: 'Mohammed'}),
  (f:Person {name: 'Michael'}),
  (g:Person {name: 'Ethan'}),
  (h:Person {name: 'Lara'}),
  (i:Person {name: 'Amir'}),
  (j:Person {name: 'Willie'}),

  (b)-[:FRIEND_OF]->(c),
  (c)-[:FRIEND_OF]->(a),
  (c)-[:FRIEND_OF]->(g),
  (c)-[:FRIEND_OF]->(h),
  (c)-[:FRIEND_OF]->(i),
  (c)-[:FRIEND_OF]->(j),
  (d)-[:FRIEND_OF]->(g),
  (f)-[:FRIEND_OF]->(e),
  (f)-[:FRIEND_OF]->(g),
  (g)-[:FRIEND_OF]->(a),
  (g)-[:FRIEND_OF]->(b),
  (g)-[:FRIEND_OF]->(h),
  (g)-[:FRIEND_OF]->(e),
  (h)-[:FRIEND_OF]->(i);

The following statement will project the graph and store it in the graph catalog.

MATCH (source:Person)
OPTIONAL MATCH (source)-[r:FRIEND_OF]->(target:Person)
RETURN gds.graph.project(
  'myGraph',
  source,
  target
)

In the following examples we will demonstrate using the CELF algorithm on this graph.

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. We will use the write mode in this example. Estimating the algorithm is useful to understand the memory impact that running the algorithm on your graph will have. When you later actually run the algorithm in one of the execution modes the system will perform an estimation. 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.

The following will estimate the memory requirements for running the algorithm:

CALL gds.influenceMaximization.celf.write.estimate('myGraph', {
  writeProperty: 'spread',
  seedSetSize: 3
})
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory

Table 13. Results
nodeCount	relationshipCount	bytesMin	bytesMax	requiredMemory
10	14	2608	2608	"2608 Bytes"

Stats

In the stats execution mode, the algorithm returns a single row containing a summary of the algorithm result. This execution mode does not have any side effects. It can be useful for evaluating algorithm performance by inspecting the computeMillis return item. In the examples below we will omit returning the timings. The full signature of the procedure can be found in the syntax section.

For more details on the stats mode in general, see Stats.

The following will run the algorithm in stats mode:

CALL gds.influenceMaximization.celf.stats('myGraph', {seedSetSize: 3})
YIELD totalSpread

Table 14. Results
totalSpread
3.76

Using stats mode is useful to inspect how different configuration options affect the totalSpread and choose ones that produce optimal spread.

Stream

In the stream execution mode, the algorithm returns the spread for nodes that are part of the seed set. This allows us to inspect the results directly or post-process them in Cypher without any side effects.

For more details on the stream mode in general, see Stream.

The following will run the algorithm, and stream results:

CALL gds.influenceMaximization.celf.stream('myGraph', {seedSetSize: 3})
YIELD nodeId, spread
RETURN gds.util.asNode(nodeId).name AS name, spread
ORDER BY spread DESC, name ASC

Table 15. Results
name	spread
"Alice"	1.46
"Ethan"	1.2
"Michael"	1.1

Note that in stream mode the result is only the seed set computed by the algorithm. The other nodes are not considered influential and are not included in the result.

Mutate

The mutate execution mode extends the stats mode with an important side effect: updating the named graph with a new influenceMaximization property containing the spread for that influenceMaximization. The name of the new property is specified using the mandatory configuration parameter mutateProperty. The result is a single summary row, similar to stats, but with some additional metrics. The mutate mode is especially useful when multiple algorithms are used in conjunction.

For more details on the mutate mode in general, see Mutate.

The following will run the algorithm, and updates the graph with the mutateProperty:

CALL gds.influenceMaximization.celf.mutate('myGraph', {
  mutateProperty: 'celfSpread',
  seedSetSize: 3
})
YIELD nodePropertiesWritten

Table 16. Results
nodePropertiesWritten
10

Stream the mutated node properties:

CALL gds.graph.nodeProperty.stream('myGraph', 'celfSpread')
YIELD nodeId, propertyValue
RETURN gds.util.asNode(nodeId).name as name, propertyValue AS spread
ORDER BY spread DESC, name ASC

Table 17. Results
name	spread
"Alice"	1.46
"Ethan"	1.2
"Michael"	1.1
"Amir"	0.0
"Ceri"	0.0
"Jack"	0.0
"Jimmy"	0.0
"Lara"	0.0
"Mohammed"	0.0
"Willie"	0.0

Note that in mutate all nodes in the in-memory graph get the spread property. The nodes that are not considered influential by the algorithm receive value of zero.

Write

The write execution mode extends the stats mode with an important side effect: writing the spread for each influenceMaximization as a property to the Neo4j database. The name of the new property is specified using the mandatory configuration parameter writeProperty. The result is a single summary row, similar to stats, but with some additional metrics. The write mode enables directly persisting the results to the database.

For more details on the write mode in general, see Write.

The following will run the algorithm, and stream results:

CALL gds.influenceMaximization.celf.write('myGraph', {
  writeProperty: 'celfSpread',
  seedSetSize: 3
})
YIELD nodePropertiesWritten

Table 18. Results
nodePropertiesWritten
10

Query the written node properties:

MATCH (n) RETURN n.name AS name, n.celfSpread AS spread
ORDER BY spread DESC, name ASC

Table 19. Results
name	spread
"Alice"	1.46
"Ethan"	1.2
"Michael"	1.1
"Amir"	0.0
"Ceri"	0.0
"Jack"	0.0
"Jimmy"	0.0
"Lara"	0.0
"Mohammed"	0.0
"Willie"	0.0

Note that in write all nodes in Neo4j graph projected get the spread property. The nodes that are not considered influential by the algorithm receive value of zero.