degree_centrality

Degree Centrality is the basic measurement of centrality that refers to the number of edges adjacent to a node. For directed graphs, we define an in-degree measure, which is defined as the number of in-coming edges, and an out-degree measure, defined as the number of out-going edges.

Let $A = (a{i,j})$ be the adjacency matrix of a directed graph. The in-degree centrality $x{i}$ of node $i$ is given by: $$x{i} = \sum_k a{k,i}$$ or in matrix form (1 is a vector with all components equal to unity): $$x = 1 A$$ The out-degree centrality $y{i}$ of node $i$ is given by: $$y{i} = \sumk a{i,k}$$ or in matrix form: $$y = A 1$$

Trait	Value
Module type	algorithm
Implementation	C++
Graph direction	directed/undirected
Edge weights	unweighted
Parallelism	sequential

Procedures

info

If you want to execute this algorithm on graph projections, subgraphs or portions of the graph, be sure to check out the guide on How to run a MAGE module on subgraphs.

get(type)

Output:

• node ➡ Node in the graph, for which Degree Centrality is calculated.
• degree ➡ Calculated degree of a node.

Usage:

CALL degree_centrality.get()
YIELD node, degree;

get_subgraph(nodes, relationships, type)

Input:

• nodes: list[node] ➡ nodes to be used in the algorithm.
• relationships: list[relationship] ➡ relationships to be considered for degree calculation.
• type: string (default="undirected") ➡ whether we are using "in", "out", or "undirected" edges.

Output:

• node ➡ Node in the graph, for which Degree Centrality is calculated.
• degree ➡ Calculated degree of a node.

Usage:

CALL degree_centrality.get()
YIELD node, degree;

Example

Step 1: Input graph

Step 2: Cypher load commands

MERGE (a:Node {id: 1}) MERGE (b:Node {id: 0}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 1}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 1}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 8}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 3}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 4}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 4}) MERGE (b:Node {id: 2}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 5}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 5}) MERGE (b:Node {id: 2}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 6}) MERGE (b:Node {id: 2}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 7}) MERGE (b:Node {id: 2}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 8}) MERGE (b:Node {id: 2}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 8}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 9}) MERGE (b:Node {id: 10}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 10}) MERGE (b:Node {id: 9}) CREATE (a)-[:RELATION]->(b);

Step 3: Running command

CALL degree_centrality.get("in")
YIELD node, degree
RETURN node, degree;

Step 4: Results

+------------------+------------------+
| node             | degree           |
+------------------+------------------+
| (:Node {id: 9})  | 1                |
| (:Node {id: 7})  | 0                |
| (:Node {id: 6})  | 0                |
| (:Node {id: 5})  | 0                |
| (:Node {id: 4})  | 0                |
| (:Node {id: 3})  | 0                |
| (:Node {id: 8})  | 1                |
| (:Node {id: 2})  | 5                |
| (:Node {id: 10}) | 7                |
| (:Node {id: 0})  | 1                |
| (:Node {id: 1})  | 1                |
+------------------+------------------+