Degree Centrality

Overview

The Degree Centrality algorithm is used to find 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. Directed self-loop is regarded as an incoming edge 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

• Degree of isolated node only depends on its self-loop. If it has no self-loop, degree is 0.
• Every self-loop is counted as 2 edges attaching to its node. Directed self-loop is viewed as an incoming edge and an outgoing edge.

Syntax

• Command: algo(degree)
• Parameters:

Examples

The example is a social network, edge property @follow.score can be used as weights:

File Writeback

UQL
algo(degree).params().write({
  file:{ 
    filename: 'degree_all'
  }
})

Statistics: total_degree = 20, average_degree = 2.25
Results: File degree_all

File
Tim,0
Bill,1
Bob,2
Sam,2
Joe,3
Anna,5
Cathy,4
Mike,3

Property Writeback

UQL
algo(degree).params({
  edge_schema_property: '@follow.score'
}).write({
  db:{ 
    property: 'degree'
  }
})

Statistics: total_degree = 40.4, average_degree = 5.05
Results: Degree for each node is written to a new property named degree, statistics is returned at the same time

Direct Return

UQL
algo(degree).params({ 
  edge_schema_property: '@follow.score',
  order: 'desc' 
}) as degree, stats
return degree, stats

Results: degree and stats

Stream Return

Example: Find 1-hop neighbors of the node with the highest degree, return all information of those neighbors

UQL
algo(degree).params({
  order: 'desc',
  limit: 1 
}).stream() as results
khop().src({_uuid == results._uuid}).depth(1) as neighbors
return neighbors{*}

Results: neighbors

Stats Return

UQL
algo(degree).params({
  direction: 'out'
}).stats() as stats
return stats

Results: stats