---
key: mechanic/puzzle--family-networks
type: mechanic
id: puzzle--family-networks
lang: en
title: 'Connections, networks and loops'
summary: >-
  The player connects nodes while respecting connectivity, crossing and
  connection-count constraints.
updatedAt: '2026-10-22'
status: active
url: 'https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-networks/'
jsonUrl: >-
  https://gamemechanics.pro/api/v1/knowledge/en/mechanic/puzzle--family-networks.json
markdownUrl: >-
  https://gamemechanics.pro/content/knowledge/en/mechanic/puzzle--family-networks.md
aliases: []
tags:
  - Puzzles
  - Mechanics catalog
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  - source-9a8abc44619bcaf4
  - source-f31552a66718c418
  - source-911a32d446c1fac0
  - source-e6546791156b5e83
sources:
  - id: source-b7eaa85f62ff3390
    title: 'Nikoli: Numberlink'
    url: 'https://www.nikoli.co.jp/en/puzzles/numberlink/'
    verifiedAt: null
  - id: source-9a8abc44619bcaf4
    title: 'Nikoli: Hashiwokakero'
    url: 'https://www.nikoli.co.jp/en/puzzles/hashiwokakero/'
    verifiedAt: null
  - id: source-f31552a66718c418
    title: 'Nikoli: Slitherlink'
    url: 'https://www.nikoli.co.jp/en/puzzles/slitherlink/'
    verifiedAt: null
  - id: source-911a32d446c1fac0
    title: 'Nikoli: Masyu'
    url: 'https://www.nikoli.co.jp/en/puzzles/masyu/'
    verifiedAt: null
  - id: source-e6546791156b5e83
    title: The Talos Principle
    url: 'https://store.steampowered.com/app/257510/'
    verifiedAt: null
relations: []
placements:
  - catalogId: puzzle
    id: family-networks
    title: Puzzles
    url: 'https://gamemechanics.pro/en/mechanics/puzzle/#family-networks'
    categoryIds:
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supersededBy: []
attributes:
  preview:
    updatedAt: '2026-10-22'
    title: 'Connections, networks and loops'
    description: >-
      The player connects nodes while respecting connectivity, crossing and
      connection-count constraints.
    image:
      src: images/mechanics/adventure-talos-principle-05.webp
      width: 1440
      height: 810
      game: The Talos Principle
      sourceUrl: 'https://store.steampowered.com/app/257510/'
      originalUrl: >-
        https://shared.akamai.steamstatic.com/store_item_assets/steam/apps/257510/ss_b42acabe63d45a11580a2949e34f305e1bd10fc7.1920x1080.jpg?t=1744327639
      credit: Croteam / Devolver Digital
      rights: >-
        Game imagery © its respective rights holders. Publisher-distributed
        Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0.
      caption: Nodes and beams form a connected system
      alt: Nodes and beams form a connected system
      markers:
        - x: 56
          'y': 30
          label: A node connects multiple directions
    tips:
      - 'Make links, crossings and disconnected sections distinguishable.'
    examples:
      - title: The Talos Principle
        url: 'https://store.steampowered.com/app/257510/'
endsAt: null
provenance: >-
  Original editorial design catalog consolidated from project discussions on
  2026-10-20. Complete discussion item lists and contextual limitations are
  preserved; linked primary sources support specific techniques, not the entire
  classification. English translation was prepared with machine assistance and
  editorial review.
license: CC-BY-4.0
codeLicense: MIT
attribution: gamemechanics.pro contributors
catalogKey: catalog/puzzle
---
# Connections, networks and loops

id: puzzle--family-networks
type: mechanic
key: mechanic/puzzle--family-networks
lang: en
status: active
url: https://gamemechanics.pro/en/knowledge/mechanic/puzzle--family-networks/

The player connects nodes while respecting connectivity, crossing and connection-count constraints.

## At a glance

![Nodes and beams form a connected system](https://gamemechanics.pro/images/mechanics/adventure-talos-principle-05.webp)

[The Talos Principle](https://store.steampowered.com/app/257510/) · Game imagery © its respective rights holders. Publisher-distributed Steam screenshot; all rights reserved. Excluded from MIT and CC BY 4.0.

1. A node connects multiple directions

- Make links, crossings and disconnected sections distinguishable.

- [The Talos Principle](https://store.steampowered.com/app/257510/)

## How it works

Build connections with conditions of connectivity, degrees of nodes and intersections.

## Variants

### Variants and applications

<a id="family-networks-variants"></a>

- Connecting network segments. Definition: Rotate or place sections connecting sources and receivers. Conventional example: Assemble a continuous pipeline. Terms: pipes; Net. <a id="variant-pipe-network"></a>
- Connection of specified pairs. Definition: Connect paired terminals by paths, observing intersection restrictions. Conditional example: Connect identical numbers with non-intersecting lines. Terms: Numberlink. <a id="variant-pair-routing"></a>
- Bridges between islands. Definition: Build a connected network with a given number of bridges at nodes. Conditional example: Connect islands using numerical clues. Terms: Hashiwokakero; Khasi. <a id="variant-bridges"></a>
- Single closed loop. Definition: Construct one loop without branches and self-intersections. Conditional example: Draw a border around the required cells. Terms: loop puzzle. <a id="variant-single-loop"></a>
- Contour by number of edges. Definition: Construct a loop by matching the number of its sides around each clue. Conventional example: Surround a square with a three with three edges. Terms: Slitherlink. <a id="variant-edge-count-loop"></a>
- Contour based on turn marks. Definition: Draw a loop through marks that define the local behavior of the line. Conditional example: Coordinate straight lines and turns for different beads. Terms: Masyu. <a id="variant-turn-clue-loop"></a>
- Network without loops. Definition: Connect all nodes without creating closed routes. Conditional example: Provide power to all stations with one tree. <a id="variant-spanning-tree"></a>
- Unraveling the graph. Definition: Move the nodes so that the edges no longer intersect. Conditional example: Separate the points, maintaining all connections. Terms: planarity; untangle. <a id="variant-untangle-graph"></a>
- Breaking selected connections. Definition: Remove or block connections, preserving the desired one and destroying the unwanted reachability. Conditional example: Isolate an infected node without shutting down the hospital. <a id="variant-network-cut"></a>
- Flow distribution. Definition: Direct a flow with restrictions on the capacity and balance of nodes. Conditional example: Deliver water to three reservoirs without overloading. <a id="variant-network-flow"></a>

## Context and limits

A wide catalog of mechanics for digital puzzles, paper logic problems and physical puzzles. Each position contains an action or rule and a conditional example of application.

## Connected materials


## Sources and provenance

Original editorial design catalog consolidated from project discussions on 2026-10-20. Complete discussion item lists and contextual limitations are preserved; linked primary sources support specific techniques, not the entire classification. English translation was prepared with machine assistance and editorial review.

- [Nikoli: Numberlink](https://www.nikoli.co.jp/en/puzzles/numberlink/) (id: source-b7eaa85f62ff3390)
- [Nikoli: Hashiwokakero](https://www.nikoli.co.jp/en/puzzles/hashiwokakero/) (id: source-9a8abc44619bcaf4)
- [Nikoli: Slitherlink](https://www.nikoli.co.jp/en/puzzles/slitherlink/) (id: source-f31552a66718c418)
- [Nikoli: Masyu](https://www.nikoli.co.jp/en/puzzles/masyu/) (id: source-911a32d446c1fac0)
- [The Talos Principle](https://store.steampowered.com/app/257510/) (id: source-e6546791156b5e83)

CC-BY-4.0 · gamemechanics.pro contributors