{"schemaVersion":1,"record":{"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"],"sourceIds":["source-b7eaa85f62ff3390","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}],"sections":[{"id":"principle","title":"How it works","body":"Build connections with conditions of connectivity, degrees of nodes and intersections."},{"id":"variants","title":"Variants","body":"### Variants and applications\n\n<a id=\"family-networks-variants\"></a>\n\n- 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>\n- 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>\n- 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>\n- 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>\n- 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>\n- 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>\n- 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>\n- 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>\n- 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>\n- 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>"},{"id":"context","title":"Context and limits","body":"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."}],"relations":[],"placements":[{"catalogId":"puzzle","id":"family-networks","title":"Puzzles","url":"https://gamemechanics.pro/en/mechanics/puzzle/#family-networks","categoryIds":["section-1"]}],"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"}}