Overview

The Degree algorithm calculates the number of edges for each node, and the sum of weights when there are weights on the edges. Since it is a shallow (≤ 1 layer) calculation for nodes, degree is the simplest and most efficient graph algorithm, which plays a vital role in scientific computing, feature extraction, supernode recognition and other fields.

Basic Concept

Degree Direction

The number of outbound edges of node is called out degree of the node; conversely, the number of inbound edges of node is called in degree of the node. If ignores the direction of edges, that is degree (or degree centrality) of the node.

Out degree of the red node in the graph above is 3, in degree is 4, degree is 7. Please note that the directed self-loop edge is regarded as an outbound edge and an inbound edge.

Edge Weight

Edge weight can be a property value of edge. When edge weights are specified, degree is the sum of all edge weights. The degree of node without specifying any edge weight can be viewed as the degree when all edge weights are 1.

After the edges are weighted, out degree of the red node in the graph above is 1 + 0.2 + 2 = 3.2, in degree is 0.5 + 0.3 + 2 + 1 = 3.8, degree is 3.2 + 3.8 = 7.

Special Case

Lonely Node, Disconnected Graph

The degree of lonely node only depends on its self-loop edge because it has no edge connected to other nodes.

Self-loop Edge

Self-loop edge is regarded as an outbound edge and an inbound edge.

Directed Edge

The direction of directed edge is the basis for calculating out degree and in degree; the direction of edge is ignored when calculating degree.

Results and Statistics

Take this small social network of 8 users as an example, nodes represent users, edges represent relationship of follow, the weight on each edge is from the property score:

Algorithm results: Calculate weighted degree for each node, return _id, degree or _uuid, degree according to the execution method

Algorithm statistics: Total degree total_degree and average degree average_degree

Command and Configuration

• Command: algo(degree)
• Configurations for the parameter params():

Algorithm Execution

Task Writeback

1. File Writeback

Example: Calculate degree of all nodes, write the algorithm results back to file

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

2. Property Writeback

Example: Calculate weighted degree of all nodes, write the algorithm results back to node property

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

3. Statistics Writeback

Example: Calculate degree of all nodes, write the algorithm statistics back to task information

algo(degree).params().write()

Direct Return

Example: Calculate weighted degree of all nodes, return the results and statistics, order the results in the descending degree

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

Streaming Return

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

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

Real-time Statistics

Example: Calculate out degree of all nodes, return the statistics

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