Harmonic Centrality

The Harmonic Centrality algorithm calculates the harmonic centrality of each vertex in the graph. Harmonic Centrality is a variant of Closeness Centrality. In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:

\[H(x)=\sum _{y\neq x}{\frac {1}{d(x,y)}}\]

For more information, see Harmonic Centrality.

Specifications

CREATE QUERY harmonic_cent(SET<STRING> v_type, SET<STRING> e_type,
    SET<STRING> re_type,INT max_hops=10, INT top_k=100, BOOL wf = TRUE,BOOL print_accum = True, STRING result_attr = "", STRING file_path = "", BOOL display_edges = FALSE)

Time complexity

The algorithm has a time complexity of \(O(E)\), where E = number of edges.

Parallel processing reduces the time needed for computation.

Parameters

Name Description Data type

v_type

Vertex types to calculate harmonic centrality for

SET<STRING>

e_type

Edge types to traverse

SET<STRING>

re_type

Reverse edge types

SET<STRING>

max_hops

The maximum number of hops the algorithm would consider for each vertex. If set to a non-positive value, the limit is ignored.

INT

top_k

Sort the scores high to low and output the highest k scores

INT

wf

If true, use the Wasserman-Faust normalization for multi-component graphs

BOOL

print_accum

If true, output JSON to standard output

BOOL

result_attr

If not empty, store centrality values (FLOAT) to this attribute

STRING

file_path

If not empty, write output to this file in CSV.

STRING

display_edges

If true, include the graph’s edges in the JSON output, so that the full graph can be displayed.

BOOL

Example

If we have the following graph, we can see that Ivy is the most central of the five vertices. Running the algorithm on the graph shows that Ivy has the highest centrality score:

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  • GSQL command

  • Result

RUN QUERY harmonic_cent(["Person"], ["Coworker"], ["Coworker"], 4, 5,
true, true, _, _, _)
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [{"top_scores": [
    {
      "score": 0.04167,
      "Vertex_ID": "Ivy"
    },
    {
      "score": 0.03571,
      "Vertex_ID": "Damon"
    },
    {
      "score": 0.03571,
      "Vertex_ID": "George"
    },
    {
      "score": 0.025,
      "Vertex_ID": "Steven"
    },
    {
      "score": 0.025,
      "Vertex_ID": "Glinda"
    }
  ]}]
}