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: $y_{i} = \sum_k a_{i,k}$ or in matrix form: $y = A 1$

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Procedures

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

cypher code for merging and creating relations...

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

+------------------+------------------+
| node             | degree           |
+------------------+------------------+
| (:Node {id: 9})  | 1                |
| ...              | ...              |
+------------------+------------------+