Syntax Inputs Outputs Query examples Sample output

Label propagation algorithm (LPA)

Label Propagation Algorithm (LPA) is an algorithm for community detection that is also used in semi-supervised machine learning for data classification.

A community structure is loosely defined as a tightly knit group of entities in social networks. LPA can be enhanced by providing a set of seed nodes, the quality of which can dramatically influence the solution quality of the found communities. If the seeds are well-selected, the quality of the solution can be good, but if not, the quality of the solution can be very bad.

See Xu T. Liu et al, Direction-optimizing label propagation and its application to community detection, and Xu T. Liu et al, Direction-optimizing Label Propagation Framework for Structure Detection in Graphs: Design, Implementation, and Experimental Analysis, and the Neo4j Label Propagation API.

The time complexity of the algorithm is O(k|E|), where |E| is the number of edges in the graph, and k is the number of iterations for the algorithm to converge. Its space complexity is O(|V|), where |V| is the number of nodes in the graph.

`.labelPropagation` syntax


CALL neptune.algo.labelPropagation(
  [source-node list (required)],
  {
    edgeLabels: [list of edge labels for filtering (optional)],
    vertexLabel: a node label for filtering (optional),
    vertexWeightProperty: a numeric node property used to weight the community ID (optional),
    vertexWeightType: numeric type of the specified vertexWeightProperty (optional),
    edgeWeightProperty: a numeric edge property used to weight the community ID (optional),
    edgeWeightType: numeric type of the specified edgeWeightProperty (optional),
    maxIterations: the maximum number of iterations to run (optional, default: 10),
    traversalDirection: traversal direction (optional, default: outbound),
    concurrency: number of threads to use (optional)
  }
)
Yield node, community
Return node, community

`.labelPropagation` inputs

a source node list (required) – type: Node[] or NodeId[]; default: none.

The node or nodes to use as the starting locations for the algorithm. Each node in the list triggers an execution of the algorithm. If an empty list is provided, the query result is also empty.

If the algorithm is called following a MATCH clause (query algo integration), the source query list is the result returned by the MATCH clause.
a configuration object that contains:
- edgeLabels (optional) – type: a list of edge label strings; example: ["route", ...]; default: no edge filtering.
  
  To filter on one more edge labels, provide a list of the ones to filter on. If no edgeLabels field is provided then all edge labels are processed during traversal.
- vertexLabel (optional) – type: string; default: none.
  
  A node label for node filtering. If a node label is provided, nodes matching the label are the only nodes that are included in the calculation, including nodes in the input list.
- vertexWeightProperty (optional) – type: string; default: none.
  
  The node weight used in Label Propagation. When vertexWeightProperty is not specified, each node's communityId is treated equally, as if the node weight were 1.0. When the vertexWeightProperty is specified without an edgeWeightProperty, the weight of the communityId for each node is the value of the node weight property. When both vertexWeightProperty and edgeWeightProperty are specified, the weight of the communityId is the product of the node property value and edge property value.
  
  Note that if multiple properties exist on the node with the name specified by vertexWeightProperty, one of those property values will be sampled at random.
- vertexWeightType (required if vertexWeightProperty is present) – type: string; valid values: "int", "long", "float", "double"; default: empty.
  
  The type of the numeric values in the node property specified by vertexWeightProperty.
  
  If vertexWeightProperty is not provided, vertexWeightType is ignored. If a node contains a numeric property with the name specified by vertexWeightProperty but its value is a different numeric type than is specified by vertexWeightType, the value is typecast to the type specified by vertexWeightType. If both vertexWeightType and edgeWeightType are given, the type specified by edgeWeightType is used for both node and edge properties.
- edgeWeightProperty (optional) – type: string; default: none.
  
  The numeric edge property used as a weight in Label Propagation. When vertexWeightProperty is not specified, the default edge weight is 1.0, so each edge is treated equally. When only edgeWeightProperty is provided, the weight of the communityId is the value of that edge property. When both vertexWeightProperty and edgeWeightProperty are present, the weight of a communityId is the product of the edge property value and the node property value.
  
  Note that if multiple properties exist on the edge with the name specified by edgeWeightProperty, one of those property values will be sampled at random.
- edgeWeightType (required if edgeWeightProperty is present) – type: string; valid values: "int", "unsignedInt", "long", "unsignedLong", "float", "double"; default: none.
  
  The type of the numeric values in the edge property specified by edgeWeightProperty.
  
  If edgeWeightProperty is not provided, edgeWeightType is ignored. If a node contains a numeric property with the name specified by edgeWeightProperty but its value is a different numeric type than is specified by edgeWeightType, the value is typecast to the type specified by edgeWeightType. If both vertexWeightType and edgeWeightType are given, the type specified by edgeWeightType is used for both node and edge properties.
- traversalDirection (optional) – type: string; default: "outbound".
  
  The direction of edge to follow. Must be one of: "inbound", "oubound", or "both".
- maxIterations (optional) – type: integer; default: 10.
  
  The maximum number of iterations to run.
- concurrency (optional) – type: 0 or 1; default: 0.
  
  Controls the number of concurrent threads used to run the algorithm.
  
  If set to 0, uses all available threads to complete execution of the individual algorithm invocation. If set to 1, uses a single thread. This can be useful when requiring the invocation of many algorithms concurrently.

`.labelPropagation` outputs

node – A key column of the input nodes.
community – A key column of the corresponding communityId values for those nodes. All the nodes with the same communityId are in the same weakly-connected component.

If the input node list is empty, the output is empty.

`.labelPropagation` query examples

This is a standalone example, where the source node list is explicitly provided in the query. It runs the algorithm over the whole graph, but only queries the component ID of one node:


CALL neptune.algo.labelPropagation(
  ["101"],
  {
    edgeLabels: ["route"], 
    maxIterations: 10,
    vertexLabel: "airport",
    vertexWeightProperty: "runways",
    vertexWeightType: "int",
    edgeWeightProperty: "dist",
    edgeWeightType: "int",
    traversalDirection: "both",
    concurrency: 2
  }
)
YIELD node, community
RETURN node, community

This is a query integration example, where .labelPropagation uses the output of a preceding MATCH clause as its source node list:


Match (n) 
CALL neptune.algo.labelPropagation(
  n,
  {
    edgeLabels: ["route"], 
    maxIterations: 10,
    vertexLabel: "airport",
    vertexWeightProperty: "runways",
    vertexWeightType: "int",
    edgeWeightProperty: "dist",
    edgeWeightType: "int",
    traversalDirection: "both",
    concurrency: 2
  }
) 
YIELD community
RETURN n, community

Warning

It is not good practice to use MATCH(n) without restriction in query integrations. Keep in mind that every node returned by the MATCH(n) clause invokes the algorithm once, which can result a very long-running query if a large number of nodes is returned. Use LIMIT or put conditions on the MATCH clause to restrict its output appropriately.

Sample `.labelPropagation` output

Here is an example of the output returned by .labelPropagation when run against the sample air-routes dataset [nodes], and sample air-routes dataset [edges], when using the following query:


"results": [{
      "node": {
        "~id": "8",
        "~entityType": "node",
        "~labels": ["airport"],
        "~properties": {
          "region": "US-TX",
          "runways": 7,
          "country": "US",
          "city": "Dallas",
          "type": "airport",
          "icao": "KDFW",
          "lon": -97.038002014160199,
          "code": "DFW",
          "lat": 32.896800994872997,
          "longest": 13401,
          "elev": 607,
          "desc": "Dallas/Fort Worth International Airport"
        }
      },
      "community": 2357352929952311
    }, {
      "node": {
        "~id": "24",
        "~entityType": "node",
        "~labels": ["airport"],
        "~properties": {
          "region": "US-CA",
          "runways": 3,
          "country": "US",
          "city": "San Jose",
          "type": "airport",
          "icao": "KSJC",
          "lon": -121.929000854492,
          "code": "SJC",
          "lat": 37.362598419189503,
          "longest": 11000,
          "elev": 62,
          "desc": "Norman Y. Mineta San Jose International Airport"
        }
      },
      "community": 2357352929952311
    }]

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Document Conventions

.wcc.mutate

.labelPropagation.mutate

Label propagation algorithm (LPA)

.labelPropagation syntax

.labelPropagation inputs

a configuration object that contains:

.labelPropagation outputs

.labelPropagation query examples