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# Induced Subgraph

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

## Overview

The Induced Subgraph algorithm is used to compute the induced subgraph of a given set of nodes in a graph. It provides a way to focus on the immediate connections and gain insights into the local structure and interactions within the selected subset of nodes.

## Concepts

### Induced Subgraph

An induced subgraph includes only the nodes from the given set and the edges that connect those nodes. As this example shows, when specifying node set S = {A, B, I, K, L, M, N}, the induced subgraph is the graph whose node set is S and whose edge set contains all edges that have both endpoints in S.

Ultipa's Induced Subgraph algorithm returns all the 1-step paths in the induced subgraph.

## Considerations

• The Induced Subgraph algorithm ignores the direction of edges but calculates them as undirected edges.

## Syntax

• Command: `algo(subgraph)`
• Parameters:
Name
Type
Spec
Default
Optional
Description
ids / uuids []`_id` / []`_uuid` / / No ID/UUID of the nodes to calculate
limit int ≥-1 `-1` Yes Number of results to return, `-1` to return all results

## Examples

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

Spec
Content
Description
filename `_id--[_uuid]--_id` One-step path in the induced subgraph:
(start node)--(edge)--(end node)
``````algo(subgraph).params({
ids: ['A','C','D','G']
}).write({
file:{
filename: 'paths'
}
})
``````

Results: File paths

``````C----A
C----D
D----A
D----A
G----G
``````

### Direct Return

Alias Ordinal
Type
Description
0 []path One-step path in the induced subgraph:
`_uuid` (start node) -- [`_uuid`] (edge) -- `_uuid` (end node)
``````algo(subgraph).params({
ids: ['A','C','D','G']
}) as subgraph
return subgraph
``````

Results: subgraph

 3----1 3----4 4----1 4----1 7----7

### Stream Return

Alias Ordinal
Type
Description
0 []path One-step path in the induced subgraph:
`_uuid` (start node) -- [`_uuid`] (edge) -- `_uuid` (end node)
``````algo(subgraph).params({
uuids: [6,7]
}).stream() as p
with pedges(p) as e
find().edges(e) as edges
return max(edges.score)
``````

Results: 5