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# Graph Centrality

✓ File Writeback ✓ Property Writeback ✓ Direct Return ✓ Stream Return ✕ Stats

## Overview

Graph centrality of a node is measured by the maximum shortest distance from the node to all other reachable nodes. This measurement, along with other measurements like closeness centrality and graph diameter, can be considered jointly to determine whether a node is literally located at the very center of the graph.

Graph centrality takes on values between 0 to 1, nodes with higher scores are closer to the center.

## Concepts

### Shortest Distance

The shortest distance of two nodes is the number of edges contained in the shortest path between them. Please refer to Closeness Centrality for more details.

### Graph Centrality

Graph centrality score of a node defined by this algorithm is the inverse of the maximum shortest distance from the node to all other reachable nodes. The formula is: where `x` is the target node, `y` is any node that connects with `x` along edges (`x` itself is excluded), `d(x,y)` is the shortest distance between `x` and `y`. In this graph, the green number and red number next to each node is the shortest distance between the node and the green node and red node. Graph centrality scores of the green and red nodes are `1/4 = 0.25` and `1/3 = 0.3333` respectively.

Regarding closeness centrality, the green node has score `8/(1+1+1+1+2+3+4+3) = 0.5`, the red node has score `8/(3+3+3+2+1+1+2+1) = 0.5`. When two nodes have the same closeness centrality score, graph centrality can be viewed as the subsidiary basis to determine which node is closer to the center.

## Considerations

• The graph centrality score of isolated nodes is 0.
• The Graph Centrality algorithm ignores the direction of edges but calculates them as undirected edges.

## Syntax

• Command: `algo(graph_centrality)`
• Parameters:
Name
Type
Spec
Default
Optional
Description
ids / uuids []`_id` / []`_uuid` / / Yes ID/UUID of the nodes to calculate, calculate for all nodes if not set
direction string `in`, `out` / Yes Direction of all edges in the shortest path, `in` for incoming direction, `out` for outgoing direction
limit int ≥-1 `-1` Yes Number of results to return, `-1` to return all results
order string `asc`, `desc` / Yes Sort nodes by the centrality score

## Examples

The example graph is as follows: ### File Writeback

Spec Content
filename `_id`,`centrality`
``````algo(graph_centrality).params().write({
file:{
filename: 'res'
}
})
``````

Results: File res

``````J,0
I,0.25
H,0.2
F,0.333333
G,0.25
D,0.2
E,0.333333
C,0.2
A,0.25
B,0.2
``````

### Property Writeback

Spec Content Write to Data Type
property `centrality` Node property `float`
``````algo(graph_centrality).params().write({
db:{
property: 'gc'
}
})
``````

Results: Centrality score for each node is written to a new property named gc

### Direct Return

Alias Ordinal
Type
Description
Columns
0 []perNode Node and its centrality `_uuid`, `centrality`
``````algo(graph_centrality).params({
ids: ['A', 'B', 'C'],
order: 'asc'
}) as gc
return gc
``````

Results: gc

_uuid centrality
2 0.2
3 0.2
1 0.25

### Stream Return

Alias Ordinal
Type
Description
Columns
0 []perNode Node and its centrality `_uuid`, `centrality`
``````algo(graph_centrality).params().stream() as gc
where gc.centrality > 0.25
return gc
``````

Results: gc

_uuid centrality
6 0.333333
5 0.333333