Graph
A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
Graph Neural Networks in Action
A graph data model specifies how entities, relationships, attributes, and constraints are represented as graph elements.
- How it is used
- Represents relationships explicitly so graph neural networks can use connections alongside entity features for prediction.
- How deep it goes
- Defines nodes, edges and adjacency matrices, sketches graph types, and points readers seeking fuller graph fundamentals to an appendix.
- Examples
- Uses a small adjacency matrix, Titanic passenger relationships and structural exploration of a Yelp review graph.
- What you can do after
- Build it from scratch by choosing entities, relationships and features, then assess whether graph structure warrants a GNN.
Authorization in Action
A relationship graph is a graph representation of entities and the relationships connecting them, including authorization-relevant relationships.
- How it is used
- Supports relationship-based authorization where sharing, delegation, ownership, and organizational connections determine access.
- How deep it goes
- Explains nodes, edges, static rules, traversal, tuples, and operational tradeoffs, while deferring graph storage internals and conditional evaluation.
- Examples
- Uses shared documents, support tickets, deployment plans, team membership, ownership, manager chains, and an OpenFGA viewer tuple.
- What you can do after
- Evaluate/understand when relationship data can drive fine-grained access and when contextual conditions require another model.
Graph Algorithms for Data Science
A graph model represents data as nodes connected by typed or untyped relationships.
- How it is used
- Reframes connected data for analysis, pattern discovery, routing, and prediction.
- How deep it goes
- Defines nodes, relationships, direction, and graph-shaped use cases before later modeling and algorithm work.
- Examples
- Uses orders, social networks, service dependencies, transportation routes, biomedical networks, and customer data.
- What you can do after
- Evaluate/understand when connected data should be represented and analyzed as a graph.
Learn Haskell by Example
A graph is a data structure consisting of nodes and edges that represent entities and relationships between them.
- How it is used
- Models word-ladder moves so a shortest-path search can connect a user’s start and end words.
- How deep it goes
- Defines nodes, edges, direction, and costs, then implements an adjacency-map directed graph; shortest-path search is deferred.
- Examples
- Uses cat-to-dog word chains, numeric directed edges, and a four-word dictionary containing an isolated dog.
- What you can do after
- Build it from scratch as a Haskell directed adjacency map with edge insertion, bulk construction, and child lookup.
Financial AI in Practice
A structure representing entities as nodes and relationships between them as edges.
- How it is used
- Expose relationships hidden by transaction-level analysis so analysts can investigate coordinated fraud.
- How deep it goes
- Defines nodes, edges, and properties, then details NetworkX construction; defers advanced GNN mathematics.
- Examples
- Illustrate chargeback users sharing merchants and a transaction-derived graph of users, IPs, devices, phones, and cards.
- What you can do after
- Build it from scratch with NetworkX using transaction tables, then inspect weighted connections and densely connected groups.
Optimization Algorithms: AI techniques for design, planning, and control problems
A graph is a nonlinear data structure consisting of vertices and edges that represent entities and relationships.
- How it is used
- Models entities and relationships for search, routing, recommendation, information retrieval, and network analysis.
- How deep it goes
- Defines graph structure, classifications, weighted edges, and Python construction, then connects graphs to search and real-world datasets.
- Examples
- Uses social networks, road networks, soccer-player data, weighted devices, and NetworkX diagrams as concrete representations.
- What you can do after
- Builds and visualizes graph structures with NetworkX and selects representations suited to relationships, weights, direction, and multiplicity.
Knowledge Graphs and LLMs in Action
A graph structure is a data representation consisting of interconnected vertices and edges.
- How it is used
- Uses interconnected data to support knowledge representation, graph learning, reasoning, classification, and relationship prediction.
- How deep it goes
- Explains vertices, edges, attributes, feature encoding, identifier mapping, PyG construction, and dataset masks without detailing graph algorithms.
- Examples
- Demonstrates healthcare entities, movie genres, user–movie ratings, and an Elliptic node-classification split.
- What you can do after
- Build it from source data by encoding features, mapping identifiers, constructing edges, and preparing graph-learning masks.
Read how Knowledge Graphs and LLMs in Action explains graph →
Advanced Algorithms and Data Structures
An abstract graph is a graph specified by its vertices and edges without a particular geometric placement.
- How it is used
- Models interconnected systems and supports route-finding, search, visualization, and semantic data organization.
- How deep it goes
- Defines graph variants, develops adjacency-list implementation, and applies graphs to routing; detailed complexity analysis is not supplied.
- Examples
- Uses delivery routes, street intersections, flow charts, printed circuit boards, and formal vertex-edge listings.
- What you can do after
- Build it from scratch with vertices, edges, weights, and adjacency lists, then model route problems for graph search.
Read how Advanced Algorithms and Data Structures explains graph →
Grokking Algorithms, Second Edition
A graph is a data structure consisting of nodes and connections that represent relationships between entities.
- How it is used
- Models connected things so path-finding algorithms can answer questions such as which route takes the fewest steps.
- How deep it goes
- Defines nodes, edges, and graph direction, then works through Python representations for plain and cost-bearing connections.
- Examples
- Uses routes, poker debts, task dependencies, family trees, and Python neighbor tables to make connections concrete.
- What you can do after
- Build it from scratch in Python as a hash table of neighbors, adding edge costs when a route needs them.
Read how Grokking Algorithms, Second Edition explains graph →
Grokking Data Structures
A graph is a data structure consisting of vertices and edges representing entities and relationships between them.
- How it is used
- Models relationships between entities, including indirect friendships that a plain user list makes cumbersome to query.
- How deep it goes
- Defines vertices, edges, and graph properties, then identifies storage approaches and briefly explains two traversal methods.
- Examples
- Uses friendships, Twitter follows, Facebook friendships, file systems, and a four-vertex edge listing.
- What you can do after
- Evaluate/understand whether relationships need a graph and how representation and traversal choices support searching them.
Natural Language Processing in Action, Second Edition
A graph is a data structure consisting of entities called nodes or vertices connected by relationships called edges.
- How it is used
- Represents relationships in social networks, semantic text analysis, and chatbot conversation flows.
- How deep it goes
- Builds an undirected embedding graph through extraction, normalization, similarity thresholding, edge creation, and visualization; contrasts directed and looping structures.
- Examples
- Uses social networks, sentence-similarity plots, chapter concept maps, chatbot flows, and Dota 2 hero descriptions.
- What you can do after
- Build it from scratch with sentence embeddings, NumPy, NetworkX, and Matplotlib, then interpret clusters or design looping dialog flows.
Read how Natural Language Processing in Action, Second Edition explains graph →
D3.js in Action, Third Edition
A graph is a mathematical structure consisting of vertices connected by edges.
- How it is used
- Represents relationships and reveals patterns in systems such as social, transportation, and linked-data networks.
- How deep it goes
- Explains nodes, edges, data separation, visualization forms, and force controls, while deferring broader network standards.
- Examples
- Uses social relationships, transportation networks, flowcharts, linked open data, node-link diagrams, and interactive organization networks.
- What you can do after
- Build it with D3 by separating nodes and edges, choosing a representation, and configuring forces for readable positions.
Data Analysis with LLMs
A graph is a data structure that represents entities as nodes and relationships as edges between them.
- How it is used
- Represents connected entities as structured data for analyzing social, road, or subway networks.
- How deep it goes
- Defines nodes, edges, labels, and node properties through examples, without detailing graph algorithms.
- Examples
- Uses social relationships and subway stations connected by line-labeled edges as examples.
- What you can do after
- Evaluate/understand it by identifying entities, relationships, and properties in connected datasets.
Machine Learning Algorithms in Depth
A graph is a mathematical or computational structure of vertices connected by edges that can represent dependencies or relationships.
- How it is used
- Represents citations for node classification and web links for page ranking.
- How deep it goes
- Defines vertices, edges, and feature matrices, then develops a transition-matrix application; graph convolution uses a library layer.
- Examples
- Uses CORA documents and citations, molecule classification, and linked web pages.
- What you can do after
- Apply it via adjacency and feature matrices to node classification, or via a transition matrix to page ranking.
Read how Machine Learning Algorithms in Depth explains graph →
Build Python Web Apps with Streamlit
A graph is a network of vertices or nodes connected by edges, and in LangGraph it models application execution and relationships between actions.
- How it is used
- Structures AI workflows that require multi-step processing, branching decisions, retrieval, tools, or conversation context.
- How deep it goes
- Explains graph components, state transformation, directed execution, and workflow input and output.
- Examples
- Uses social-network relationships and a sum-of-squares workflow to make graph structure concrete.
- What you can do after
- Build a LangGraph workflow by organizing actions as nodes, connecting them with directed edges, and passing application state between steps.
Read how Build Python Web Apps with Streamlit explains graph →
Fabulous Adventures in Data Structures and Algorithms
A graph is a data structure consisting of vertices connected by directed or undirected edges.
- How it is used
- Models relationships between nodes and supplies the structure needed for graph coloring and backtracking search.
- How deep it goes
- Defines nodes, edges, invariants, cliques, and an immutable C# representation, then applies the structure to Sudoku.
- Examples
- Uses South American countries, friendship cliques, and an 81-node Sudoku graph with row, column, and box cliques.
- What you can do after
- Build it from scratch as an immutable generic C# graph and encode Sudoku constraints as nodes, edges, and cliques.
Read how Fabulous Adventures in Data Structures and Algorithms explains graph →
Sutskever's List
A graph is a data structure composed of entities represented as nodes and relationships represented as edges.
- How it is used
- Represent molecules as graph data for supervised prediction of molecular properties.
- How deep it goes
- Connects node-edge representation to iterative message passing and pooled graph-level prediction.
- Examples
- Uses molecules, atoms, bonds, spatial distances, three-dimensional orientation, and predictions of energy, dipole, or gap.
- What you can do after
- Understand how molecular structure becomes input for graph-level property prediction through message passing and pooling.
Grokking AI Algorithms, Second Edition
A graph is a data structure consisting of entities represented as vertices and relationships represented as edges.
- How it is used
- Models relationships and search problems involving paths, networks, web links and social connections.
- How deep it goes
- Defines nodes, edges, weights, categories and several representations, but stops short of implementation code or algorithmic analysis.
- Examples
- Uses road trips, computer networks, web crawlers, social relationships, course prerequisites, teams, cheese tastings and city distances.
- What you can do after
- Build it from scratch by choosing a graph category and representing its nodes and relationships for algorithmic processing.
Read how Grokking AI Algorithms, Second Edition explains graph →
Deep Learning with Python, Third Edition
A node-and-edge structure used here to represent how model layers are connected, including branches and merges.
- How it is used
- Represents nonlinear model topologies that exceed a single input-to-output layer sequence.
- How deep it goes
- Explains graph construction through symbolic tensors, layer connections, model inputs and outputs, and topology plotting.
- Examples
- Uses a ticket classifier with three inputs, concatenated features, and priority and department outputs.
- What you can do after
- Apply it via Keras Functional API to build, inspect, and plot models with branches, merges, and multiple outputs.
Read how Deep Learning with Python, Third Edition explains graph →
Terraform in Depth: Infrastructure as Code with Terraform and OpenTofu
A graph is a representation of entities and the relationships between them as vertices and edges.
- How it is used
- Uses dependency graphs to represent Terraform systems and plans and to support configuration and plan debugging.
- How deep it goes
- Defines nodes, edges, direction, and cycles, then demonstrates visualization but stops short of graph-construction internals.
- Examples
- Uses family trees, organization charts, social media relationships, Terraform TLS modules, and DOT-to-image commands.
- What you can do after
- Diagnose resource dependencies and circular-dependency errors by generating Terraform graph visualizations.
Read how Terraform in Depth: Infrastructure as Code with Terraform and OpenTofu explains graph →
Digital Twins in Action
A data structure consisting of nodes and edges that represent entities and relationships between them.
- How it is used
- Structures physical infrastructure in digital twins to support navigation and provide a network for travel-time prediction.
- How deep it goes
- Defines nodes and edges through roads and bridges, then describes semantic extensions without providing graph algorithms or implementation steps.
- Examples
- Illustrates directed roads and intersections in Google Maps and the seven bridges of Königsberg.
- What you can do after
- Evaluate/understand how graph connections support navigation and how an ontology gives those connections queryable meaning.
Related concepts
- edgehas part · An edge is a graph connection between two vertices that represents a relationship and may be directed, labeled, or weighted.
- nodehas part · A node is a discrete element in a structured system, such as a graph, tree, network, or distributed system, representing an entity, state, component, or computational unit and potentially connected to other elements.
- directed graphincludes · A directed graph is a graph whose edges have an orientation from a source vertex to a destination vertex.
- undirected graphincludes · An undirected graph is a graph whose edges have no orientation, so each edge connects its endpoints symmetrically.
- treeincludes · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
- graph neural networkused by · A graph neural network is a neural-network model that learns representations or predictions from graph-structured data by combining information from connected entities.
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