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# Degree Centrality

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

## Overview

The Degree Centrality algorithm is used to find important nodes in the network, it measures the number of incoming and/or outgoing edges incident to the node, or the sum of weights of those edges. Degree is the simplest and most efficient graph algorithm since it only considers the 1-hop neighborhood of nodes. Degree plays a vital role in scientific computing, feature extraction, supernode recognition and other fields.

## Concepts

### In-Degree and Out-Degree

The number of incoming edges a node has is called its in-degree; accordingly, the number of outgoing edges is called out-degree. If ignores edge direction, it is degree.

In this graph, the red node has in-degree of 4 and out-degree of 3, and its degree is 7. Directed self-loop is regarded as an incoming edge and an outgoing edge.

### Weighted Degree

In many applications, each edge of a graph has an associated numeric value, called weight. In weighted graph, weighted degree of a node is the sum of weights of all its neighbor edges. Unweighted degree is equivalent to when all edge weights are 1.

In this weighted graph, the red node has weighted in-degree of `0.5 + 0.3 + 2 + 1 = 3.8` and weighted out-degree of `1 + 0.2 + 2 = 3.2`, and its weighted degree is `3.2 + 3.8 = 7`.

## Considerations

• Degree of isolated node only depends on its self-loop. If it has no self-loop, degree is 0.
• Every self-loop is counted as 2 edges attaching to its node. Directed self-loop is viewed as an incoming edge and an outgoing edge.

## Syntax

• Command: `algo(degree)`
• 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
edge_schema_property []`@<schema>?.<property>` Numeric type, must LTE / Yes Edge property(-ies) to use as edge weight(s), where the values of multiple properties are summed up
direction string `in`, `out` / Yes `in` for in-degree, `out` for out-degree
limit int ≥-1 `-1` Yes Number of results to return, `-1` to return all results
order string `asc`, `desc` / Yes Sort nodes by the size of degree

## Examples

The example is a social network, edge property @follow.score can be used as weights:

### File Writeback

Spec Content
filename `_id`,`degree`
``````algo(degree).params().write({
file:{
filename: 'degree_all'
}
})
``````

Statistics: total_degree = 20, average_degree = 2.25
Results: File degree_all

``````Tim,0
Bill,1
Bob,2
Sam,2
Joe,3
Anna,5
Cathy,4
Mike,3
``````

### Property Writeback

Spec Content Write to Data Type
property `degree` Node property `double`
``````algo(degree).params({
edge_schema_property: '@follow.score'
}).write({
db:{
property: 'degree'
}
})
``````

Statistics: total_degree = 40.4, average_degree = 5.05
Results: Degree for each node is written to a new property named degree, statistics is returned at the same time

### Direct Return

Alias Ordinal
Type
Description Columns
0 []perNode Node and its degree `_uuid`, `degree`
1 KV Total and average degree of all nodes `total_degree`, `average_degree`
``````algo(degree).params({
edge_schema_property: '@follow.score',
order: 'desc'
}) as degree, stats
return degree, stats
``````

Results: degree and stats

_uuid degree
3 11.1
2 6.5
4 6.1
6 5.2
1 4.9
5 4.3
7 2.3
8 0
total_degree average_degree
40.4 5.05

### Stream Return

Alias Ordinal
Type
Description Columns
0 []perNode Node and its degree `_uuid`, `degree`

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{*}
``````

Results: neighbors

_id _uuid
Bill 7
Sam 5
Joe 4
Cathy 2
Mike 1

### Stats Return

Alias Ordinal
Type
Description Columns
0 KV Total and average degree of all nodes `total_degree`, `average_degree`
``````algo(degree).params({
direction: 'out'
}).stats() as stats
return stats
``````

Results: stats

total_degree average_degree
10 1.25