Edge
An edge is a graph connection between two vertices that represents a relationship and may be directed, labeled, or weighted.
Authorization in Action
A relationship edge is a graph connection that records an association between entities or between an entity and a resource.
- How it is used
- Records authorization-relevant relationships that dynamic policies query to decide access.
- How deep it goes
- Explains edge modeling, graph updates, and membership tradeoffs, while deferring storage-specific implementation details.
- Examples
- Uses document ownership and viewing, team membership, and employee-customer-document collaboration graphs.
- What you can do after
- Apply it via OpenFGA by defining relations, storing tuples, and checking graph-based permissions.
D3.js in Action, Third Edition
A network edge, also called a link, is a connection between two nodes in a network or graph.
- How it is used
- Represents relationships between nodes when building and comparing network visualizations.
- How deep it goes
- Defines edge lists, direction, weights, and visual encodings, then implements SVG tree and arc-diagram links with D3.
- Examples
- Uses Romeo and Juliet character co-occurrence, weighted arc-diagram links, and language-tree paths.
- What you can do after
- Build it from scratch as source-target data and render it as weighted SVG paths with D3.
Grokking Data Structures
A tree link is a connection from one tree node to another tree node, typically representing a parent-child relationship.
- How it is used
- Connects nodes to express parent–child relationships and paths through a tree.
- How deep it goes
- Defines links through parents, children, leaves, and unique paths, but does not implement tree links.
- Examples
- Illustrates a root linked to children valued 2 and 8, then contrasts friendship edges in a graph.
- What you can do after
- Evaluate/understand it by identifying parents, children, leaves, and paths from a tree’s links.
Advanced Algorithms and Data Structures
An edge is a connection between two vertices in a graph, represented here by an ordered pair of endpoints.
- How it is used
- Models relationships, permitted movement, routes, recommendations, databases, circuit boards, and visual process flows.
- How deep it goes
- Defines endpoints, direction, loops, multiplicity, and weights, then applies edges to route and visualization models.
- Examples
- Uses product associations, ordered-pair listings, delivery maps, flow charts, circuit boards, and graph drawings.
- What you can do after
- Build graph models by selecting endpoints, direction, loops, multiplicity, and weights for concrete applications.
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Graph Neural Networks in Action
An edge is a graph element representing a relationship or connection between nodes and optionally carrying attributes or properties.
- How it is used
- Represents relationships chosen when converting raw or tabular data into a graph for analysis and GNN training.
- How deep it goes
- Defines links, illustrates binary and weighted adjacency entries, and discusses graph-construction choices without specifying edge-level model internals.
- Examples
- Uses passenger family and cabin ties, investor co-investment, and job-candidate referrals to illustrate possible edges.
- What you can do after
- Build it from scratch by choosing relationships, direction, weights, and attributes before preparing a graph for a GNN.
Knowledge Graphs and LLMs in Action
A relationship, or edge, is a graph connection representing a meaningful association between nodes.
- How it is used
- Connects entities in knowledge graphs, individuals in fraud networks, or agent functions in executable workflows.
- How deep it goes
- Explains semantic direction, undirected modeling, properties, and dynamic routing, but does not develop edge algorithms independently.
- Examples
- Uses healthcare entity associations, Jane Austen–WORKS_FOR–Google, a NetworkX fraud network, and LangGraph agent routing.
- What you can do after
- Build graph connections in NetworkX, model extracted relations consistently, or configure execution paths in LangGraph.
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Natural Language Processing in Action, Second Edition
An edge is a graph relationship connecting two nodes or vertices.
- How it is used
- Represents relationships in social networks, semantic graphs, knowledge graphs, and chatbot conversation designs.
- How deep it goes
- Explains directed and undirected forms, weighted similarity connections, and graph construction, but defers general graph algorithms.
- Examples
- Uses friendship, social-network following, sentence similarity, knowledge triples, and chatbot state transitions as concrete edge examples.
- What you can do after
- Build it from scratch by connecting nodes with NetworkX edges, assigning weights, and plotting the resulting graph.
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Learn Haskell by Example
An edge is a graph relationship that connects one node to another, optionally with a specified direction.
- How it is used
- Uses edges to build a word-ladder graph whose paths can be searched for a shortest transformation chain.
- How deep it goes
- Defines directed and undirected edges, then implements directed-edge insertion, duplicate handling, bulk insertion, and child lookup.
- Examples
- Uses English word ladders and a directed integer graph with edges such as `(3,2)` and `(3,1)`.
- What you can do after
- Build from scratch a directed graph API that adds edges and retrieves a node's connected children.
Financial AI in Practice
A connection between vertices in a graph, representing a relationship or interaction.
- How it is used
- Connects financial entities so investigators can find relationships and coordinated activity missed by transaction-level analysis.
- How deep it goes
- Defines edges and their properties, then shows transaction co-occurrence, weighted edge construction, and graph-count checks in NetworkX.
- Examples
- Uses user–merchant transactions, shared devices or IPs, account transfers, and dated chargeback connections.
- What you can do after
- Build it from scratch with NetworkX by connecting transaction entities, counting repeated links, and checking graph statistics before community detection.
Optimization Algorithms: AI techniques for design, planning, and control problems
An edge is a graph connection between two vertices, optionally representing a directed or weighted relationship.
- How it is used
- Models relationships and transitions between vertices for graph construction, traversal, routing, and search.
- How deep it goes
- Defines edge direction, multiplicity, and weights, then connects them to NetworkX construction and shortest-path search.
- Examples
- Uses NetworkX graphs, parallel roads, device connections, social relationships, and University of Toronto road segments.
- What you can do after
- Build graph connections with NetworkX and select direction, multiplicity, or weights for routing and search problems.
AI-Powered Search
An edge is a graph element representing a relationship between two nodes.
- How it is used
- Models relationships in knowledge graphs and enables traversal-based inference in search applications.
- How deep it goes
- Defines edges, explains traversal and document-set construction, and demonstrates typed relationships without detailing graph-storage internals.
- Examples
- Uses an author-paper-conference graph and a Jean Grey traversal through an "in love with" relationship.
- What you can do after
- Apply it via SKG traversal to model or discover relationships from document-set intersections and relationship queries.
Build Python Web Apps with Streamlit
A graph edge is a connection between two graph nodes that represents a relationship or execution transition.
- How it is used
- Models relationships between objects and execution flow between state-transforming actions.
- How deep it goes
- Explains graph connections, direction, execution order, and state transfer without detailing implementation APIs.
- Examples
- Uses social-network friendships, LangGraph workflows, and a sum-of-squares computation as concrete graph examples.
- What you can do after
- Apply it via LangGraph to represent which application actions execute next and exchange updated state.
Read how Build Python Web Apps with Streamlit explains edge →
Digital Twins in Action
A geometric edge is a line segment connecting two vertices in a polygonal model.
- How it is used
- Defines connections between mesh vertices that bound polygonal surfaces in 3D digital-twin models.
- How deep it goes
- Defines edges among mesh primitives and illustrates their connections through an OBJ cube, without separate edge declarations or edge-processing algorithms.
- Examples
- Uses a cube defined by OBJ vertex, normal, and face entries to make its edges identifiable.
- What you can do after
- Build it from scratch by defining vertices, faces, and normals in a text-based 3D model and identifying the edges joining face vertices.
AI Agents and Applications
An edge is a LangGraph graph connection that determines how execution moves between nodes, optionally according to a condition.
- How it is used
- Connects LangGraph processing nodes and routes execution through fixed or state-dependent workflow paths.
- How deep it goes
- Defines fixed, conditional, entry, and terminating transitions with implementation examples, but does not detail edge internals.
- Examples
- Uses research refinement, result summarization, and LLM-tool loops to demonstrate fixed and runtime-selected transitions.
- What you can do after
- Apply it via LangGraph to construct directed workflows, route on runtime state, terminate execution, and debug data flow.
Spring in Action, Sixth Edition
An entity relationship is an association between persisted domain entities represented in an application's data model.
- How it is used
- Models associations between persisted domain entities when implementing reactive persistence.
- How deep it goes
- Explains relationship-storage alternatives and their trade-offs, but stops short of implementing relationship loading.
- Examples
- Uses Taco ingredient IDs and TacoOrder taco IDs stored in sets and database array columns.
- What you can do after
- Apply it via Spring Data R2DBC by choosing an explicit storage strategy for related entity identifiers.
Sutskever's List
An edge is a graph element representing a relationship between two nodes and optionally carrying attributes.
- How it is used
- Represents molecular bonds in graph-based learning for predicting molecular properties.
- How deep it goes
- Defines molecular edges and explains virtual connections for message propagation without detailing their implementation.
- Examples
- Uses molecular bonds as physical edges and added virtual edges between unconnected atoms.
- What you can do after
- Understand how physical and virtual edges support message passing in molecular graphs.
Grokking Algorithms, Second Edition
An edge is a connection between two vertices in a graph, optionally representing a direction from one vertex to another.
- How it is used
- Models relationships between nodes for network searches, dependencies, and hierarchical structures.
- How deep it goes
- Explains direction, neighbor terminology, Python representation, runtime impact, dependencies, and trees through concrete examples.
- Examples
- Uses poker debts, social connections, Python adjacency lists, morning-task dependencies, and family trees.
- What you can do after
- Build it from scratch by representing directed graph edges with Python hash tables and lists.
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Fabulous Adventures in Data Structures and Algorithms
An edge is a graph or tree connection from one node to another that may carry a label.
- How it is used
- Represents character-labeled transitions while traversing and constructing a trie.
- How deep it goes
- Defines labels, targets, traversal, lookup, and creation, but does not develop general graph algorithms.
- Examples
- Uses a C# trie node whose Dictionary<char, Node> stores outgoing character-labeled edges.
- What you can do after
- Apply edge accessors to traverse, inspect, and extend a mutable trie node.
Read how Fabulous Adventures in Data Structures and Algorithms explains edge →
Related concepts
- graphpart of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
- weighted edgeincludes · A weighted edge is a graph edge associated with a value representing a cost, distance, capacity, or other connection attribute.
- cycleincludes · A cycle is a recurring sequence of connected elements or events that returns to an earlier point, forming a loop.
- knowledge graphpart of · A knowledge graph is a graph-structured representation of entities and their semantically meaningful relationships, often including associated attributes or facts.
- many-to-many relationshipincludes · A many-to-many relationship is an association in which multiple instances of each participating entity can relate to multiple instances of the other.
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