{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.bridge-q2532492","code":"thing-q2532492","url":"https://ver.cy/models/thing/q2532492/","name":"bridge","alternateNames":[],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.REL"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In graph theory, an edge whose removal increases the number of connected components of a graph, so that it is the only path between the two parts it joins, also called a cut-edge or isthmus; bridges are found by depth-first search algorithms and matter for network reliability, since a bridge is a single point of failure between two regions of a network.","purpose":"Let an agent define bridges in graphs, explain algorithms to find them, relate them to connectivity and network reliability, and separate other senses of bridge.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Cut-edge","Not on a cycle","Connectivity-critical","Algorithmically detectable"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What a bridge is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a bridge in a graph, and why is an edge a bridge exactly when it lies on no cycle?","kind":"definition"},{"text":"How does a bridge differ from a cut vertex?","kind":"definition"}]}]},{"id":"senses","name":"Senses","description":"Other senses.","findings":[{"id":"senses-finding","name":"Senses","description":"Other senses.","questions":[{"text":"Is a physical bridge, a network bridge device, the card game or the graph concept meant?","kind":"boundary"},{"text":"Which entry fits?","kind":"action"}]}]}]},{"id":"find","name":"Find","description":"Finding bridges.","layers":[{"id":"algorithm","name":"Algorithm","description":"Bridge-finding algorithms.","findings":[{"id":"algorithm-finding","name":"Algorithm","description":"Algorithms.","questions":[{"text":"How does the depth-first search algorithm with low-link values find all bridges in linear time?","kind":"definition"},{"text":"How can it be implemented for this graph?","kind":"action"}]}]},{"id":"components","name":"Components","description":"2-edge-connected components.","findings":[{"id":"components-finding","name":"Components","description":"Components.","questions":[{"text":"How are 2-edge-connected components computed from bridges?","kind":"definition"},{"text":"What is the bridge tree of a graph?","kind":"definition"}]}]}]},{"id":"apply","name":"Apply","description":"Applications.","layers":[{"id":"reliability","name":"Reliability","description":"Network reliability.","findings":[{"id":"reliability-finding","name":"Reliability","description":"Reliability.","questions":[{"text":"Which links in this network are bridges and therefore single points of failure?","kind":"action"},{"text":"How can redundancy remove them?","kind":"action"}]}]},{"id":"other","name":"Other","description":"Other applications.","findings":[{"id":"other-finding","name":"Other","description":"Other applications.","questions":[{"text":"How are bridges used in analysing social, transport and biological networks?","kind":"provenance"},{"text":"How do directed graphs change the concept?","kind":"definition"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching.","layers":[{"id":"teach","name":"Teach","description":"Teaching bridges.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can bridges and connectivity be taught with small examples?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"Who introduced bridge-finding algorithms, and how have they evolved?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Find bridges in a graph using standard algorithms and report them.","Flag bridges in networks it is authorized to analyse as single points of failure."],"mustNot":["Confuse the graph-theory sense with a physical bridge or the card game.","Publish the bridges of a real infrastructure or communication network in a way that helps someone attack it.","Report a graph as free of bridges without having checked it completely."],"requiresHuman":["Using bridge analysis to decide which links of a real network to cut, remove or protect."]},"ethics":{"considerations":["Bridges in real networks show where one failure cuts off whole communities.","The same analysis can protect a network or target it."],"affectedParties":["Users of networks","Network operators","Communities served by a single link"]},"owners":{"steward":"Nobody: a mathematical concept; the operator of a network answers for its use there.","roles":[],"masterSystems":[]},"relations":[{"target":"Q3297804","type":"parent","note":"registry parent class"},{"target":"edge","type":"related","note":"category"},{"target":"graph theory","type":"related","note":"field"},{"target":"connectivity","type":"related","note":"the property affected"},{"target":"ordered pair","type":"related","note":"edges as pairs"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.bridge-q2532492","Wikidata: Q2532492 (https://www.wikidata.org/wiki/Q2532492)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Edge whose removal disconnects the graph","Not part of any cycle","A cut vertex is the vertex analogue","Not physical; an edge in a graph diagram whose removal disconnects parts."]},"capabilities":{"applicability":"required","items":["define bridges and related concepts","explain bridge-finding algorithms","apply to network reliability","separate other senses"]},"hazards":{"applicability":"required","items":["Confusing with physical bridges or the card game","Inefficient detection in large graphs","Ignoring bridges in network design"]},"interfaces":{"applicability":"required","items":["Mathematical terminology conventions"]},"context":{"applicability":"required","items":["Identifying critical edges in graphs and networks.","bridges in undirected graphs","bridges in trees, where every edge is a bridge","bridge-related concepts such as 2-edge-connected components","strong bridges in directed graphs"]}},"sources":[{"title":"Wikidata item Q2532492: bridge","url":"https://www.wikidata.org/wiki/Q2532492","note":"identity and sense of the item"},{"title":"Wikipedia: Bridge (graph theory)","url":"https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29","note":"general description of the item"}],"openQuestions":["Should cut vertices be a separate entry?","How should algorithm references be linked?","How should other senses be split?"],"resources":{"spec":"/models/things/publications/thing-q2532492/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q2532492/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T21:25:36Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:57+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}