Degree Centrality

Overview

The Degree Centrality finds important nodes in the network, it measures the number of incoming and/or outgoing edges incident to the node, or the sum of weights of those edges. Degree is the simplest and most efficient graph algorithm since it only considers the 1-hop neighborhood of nodes. Degree plays a vital role in scientific computing, feature extraction, supernode recognition and other fields.

Concepts

In-Degree and Out-Degree

The number of incoming edges a node has is called its in-degree; accordingly, the number of outgoing edges is called out-degree. If ignores edge direction, it is degree.

In this graph, the red node has in-degree of 4 and out-degree of 3, and its degree is 7. A directed self-loop is regarded as both an incoming and an outgoing edge.

Weighted Degree

In many applications, each edge of a graph has an associated numeric value, called weight. In weighted graph, weighted degree of a node is the sum of weights of all its neighbor edges. Unweighted degree is equivalent to when all edge weights are 1.

In this weighted graph, the red node has weighted in-degree of 0.5 + 0.3 + 2 + 1 = 3.8 and weighted out-degree of 1 + 0.2 + 2 = 3.2, and its weighted degree is 3.2 + 3.8 = 7.

Considerations

• The degree of an isolated node depends only on its self-loop. If it has no self-loop, degree is 0.
• Every self-loop is counted as two edges attaching to its node. Directed self-loop is viewed as an incoming edge and an outgoing edge.

Example Graph

GQL
INSERT (Mike:user {_id: "Mike"}), (Cathy:user {_id: "Cathy"}),
       (Anna:user {_id: "Anna"}), (Joe:user {_id: "Joe"}),
       (Sam:user {_id: "Sam"}), (Bob:user {_id: "Bob"}),
       (Bill:user {_id: "Bill"}), (Tim:user {_id: "Tim"}),
       (Mike)-[:follow {score: 1.9}]->(Cathy), (Cathy)-[:follow {score: 1.8}]->(Mike),
       (Mike)-[:follow {score: 1.2}]->(Anna), (Cathy)-[:follow {score: 2.6}]->(Anna),
       (Cathy)-[:follow {score: 0.2}]->(Joe), (Joe)-[:follow {score: 4.2}]->(Anna),
       (Bob)-[:follow {score: 1.7}]->(Joe), (Sam)-[:follow {score: 3.5}]->(Bob),
       (Sam)-[:follow {score: 0.8}]->(Anna), (Bill)-[:follow {score: 2.3}]->(Anna)

Parameters

Run Mode

Returns:

Normalized degree for all nodes:

GQL
CALL algo.degree({
  normalized: true,
  order: "desc"
}) YIELD nodeId, degree, score, inDegree, outDegree

Result:

Out-degree top 3:

GQL
CALL algo.degree({
  direction: "out",
  order: "desc",
  limit: 3
}) YIELD nodeId, degree

Result:

Weighted degree:

GQL
CALL algo.degree({
  weight: "score",
  order: "desc"
}) YIELD nodeId, degree, weightScores

Result:

Stream Mode

Returns the same columns as run mode, streamed for memory efficiency.

Find neighbors of the node with the highest out-degree:

GQL
CALL algo.degree.stream({
  direction: "out",
  order: "desc",
  limit: 1
}) YIELD nodeId, degree
MATCH (src WHERE src._id = nodeId)-(neigh)
RETURN DISTINCT neigh._id

Result:

Stats Mode

Returns:

GQL
CALL algo.degree.stats() YIELD nodeCount, minScore, maxScore, avgScore

Result:

Write Mode

Computes results and writes them back to node properties. The write configuration is passed as a second argument map.

Write parameters:

Writable columns:

Returns:

GQL
CALL algo.degree.write({}, {
  db: {
    property: "deg_score"
  }
}) YIELD task_id, nodesWritten, computeTimeMs, writeTimeMs