# Change Nickname

Current Nickname:

• Ultipa Graph V4

Standalone

The MAC address of the server you want to deploy.

Cancel
Apply
 ID Product Status Cores Applied Validity Period(days) Effective Date Excpired Date Mac Address Apply Comment Review Comment
Close
Profile
• Full Name:
• Phone:
• Company:
• Company Email:
• Country:
• Language:
Apply

You have no license application record.

Apply
Certificate Issued at Valid until Serial No. File
Serial No. Valid until

Not having one? Apply now! >>>

Product Created On ID Amount (USD) Invoice
Product Created On ID Amount (USD) Invoice

No Invoice

# k-Edge Connected Components

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

## Overview

The k-Edge Connected Components algorithm aims to find groups of nodes that have strong interconnections based on their edges. By considering the connectivity of edges rather than just the nodes themselves, the algorithm can reveal clusters or communities within the graph where nodes are tightly linked to each other. This information can be valuable for various applications, including social network analysis, web graph analysis, biological network analysis, and more.

Related material of the algorithm:

## Concepts

### Edge Connectivity

The edge connectivity of a graph is a measure that quantifies the minimum number of edges that need to be removed in order to disconnect the graph or reduce its connectivity. It represents the resilience of a graph against edge failures. Given a graph G = (V, E), G is k-edge connected if it remains connected after the removal of any k-1 or fewer edges from G.

The edge connectivity can also be interpreted as the maximum number of edge-disjoint paths between any two nodes in the graph. If the edge connectivity of a graph is k, it means that there are k edge-disjoint paths between any pair of nodes in the graph.

Below shows a 3-edge connected graph and the edge-disjoint paths between each node pair.

Edge-disjoint paths are paths that do not have any edge in common.

### k-Edge Connected Components

Instead of determining whether the entire graph G is k-edge connected, the k-Edge Connected Components algorithm is interested in finding the maximal subsets of nodes Vi ⊆ V, where the subgraphs induced by Vi are k-edge connected.

For example, in social networks, finding a group of people who are strongly connected is more important than computing the connectivity of the entire social network.

## Considerations

• For k = 1, this problem is equivalent to finding the connected components of G.
• The k-Edge Connected Component algorithm ignores the direction of edges but calculates them as undirected edges.

## Syntax

• Command: `algo(kcc)`
• Parameters:
Name
Type
Spec
Default
Optional
Description
k int >1 / No There are k edge-disjoint paths between any pair of nodes in the k-edge connected components

## Examples

The example graph is as follows:

### File Writeback

Spec
Content
Description
filename `_id`,`_id`,... The IDs of nodes that are contained in each k-edge connected component
``````algo(kcc).params({
k: 3
}).write({
file:{
filename: 'result'
}
})
``````

Results: File result

``````F,G,I,H,
J,K,M,L,
``````