graph theory | BestHub

Model Perspective

Feb 10, 2025 · Operations

Master Task Scheduling with AOV and AOE Networks: From Class Timetables to Project Plans

This article explains how AOV (Activity on Vertex) and AOE (Activity on Edge) networks model task dependencies and durations, showing practical examples for course scheduling and construction project management, and demonstrates topological sorting and critical‑path analysis to create clear, conflict‑free schedules.

AOE networkAOV networkgraph theory

0 likes · 7 min read

Master Task Scheduling with AOV and AOE Networks: From Class Timetables to Project Plans

Model Perspective

Sep 10, 2024 · Fundamentals

Why Euler’s Polyhedron Formula Is the Gateway to Modern Topology

Euler’s polyhedron formula V‑E+F=2, celebrated as the second most beautiful theorem, links simple geometric counts to deep topological insights, inspiring centuries of proofs, applications from dice to soccer balls, and paving the way for graph theory, the four‑color theorem, and modern topology.

Eulergraph theorymathematics history

0 likes · 10 min read

Why Euler’s Polyhedron Formula Is the Gateway to Modern Topology

Model Perspective

Sep 4, 2024 · Fundamentals

Modeling Family Financial Crises with Graph Theory: Insights into System Resilience

The article uses the TV drama “凡人歌” to illustrate how a family’s financial shock can be abstracted as a complex, coupled system, examining its feedback loops, risk‑resilience, and how graph‑theoretic modeling of members and relationships reveals pathways of impact and potential mitigation strategies.

family dynamicsgraph theoryrisk analysis

0 likes · 10 min read

Modeling Family Financial Crises with Graph Theory: Insights into System Resilience

Model Perspective

Jul 4, 2024 · Fundamentals

Unlock Your Inner Mathematician: Exploring Voronoi, Graph Theory, and More

The article invites readers to revive the mathematician, physicist, economist and other scholarly personas within themselves, showing how interdisciplinary concepts such as Voronoi diagrams, graph theory, knot theory, non‑Euclidean geometry, fuzzy logic and fractal dimensions can enrich everyday problem‑solving and inspire a love of mathematics.

InterdisciplinaryVoronoi diagramfractal dimension

0 likes · 21 min read

Unlock Your Inner Mathematician: Exploring Voronoi, Graph Theory, and More

Model Perspective

Jul 2, 2024 · Fundamentals

How to Quantify Tight vs Loose Coupling with Graph Theory

Understanding tight and loose coupling in system design, this article explains their trade‑offs, introduces a coupling degree metric based on graph theory, demonstrates calculations with example module dependencies, and discusses when each approach is preferable for performance, maintainability, and scalability.

couplinggraph theoryloose coupling

0 likes · 6 min read

How to Quantify Tight vs Loose Coupling with Graph Theory

Model Perspective

May 20, 2024 · Artificial Intelligence

How Dimensionality Reduction and Graph Theory Simplify Complex Systems

The article explains how dimensionality reduction techniques—such as PCA, LDA, and t‑SNE—combined with graph theory can transform high‑dimensional data into simpler, low‑dimensional representations, enabling clearer analysis of complex systems like neural networks and image data, and enhancing machine‑learning efficiency.

Data Visualizationdimensionality reductiongraph theory

0 likes · 6 min read

How Dimensionality Reduction and Graph Theory Simplify Complex Systems

Model Perspective

May 18, 2024 · Fundamentals

How Graph Theory Reveals Hidden Criminal Networks: Centrality Measures Explained

By modeling crime relationships as graphs and applying centrality metrics such as degree, betweenness, and closeness, investigators can mathematically identify key suspects, trace financial flows, and prioritize targets, demonstrating how graph theory transforms complex criminal networks into actionable intelligence.

centralitycrime investigationgraph theory

0 likes · 10 min read

How Graph Theory Reveals Hidden Criminal Networks: Centrality Measures Explained

Model Perspective

Jan 14, 2024 · Fundamentals

How Graph Theory Can Predict Global War Risks: A Quantitative Model

This article presents a graph‑theory based mathematical model that treats nations as nodes and their relationships as weighted edges, using centrality metrics to quantitatively assess and forecast potential war risks, illustrated with a 2024 case study of key global regions and an adjacency matrix.

centrality metricsgraph theoryinternational relations

0 likes · 9 min read

How Graph Theory Can Predict Global War Risks: A Quantitative Model

Zhuanzhuan Tech

Nov 15, 2023 · Information Security

Association Graph for Fraud Detection: Theory, Architecture, and Applications

This article explains the concept of association graphs, their foundation in graph theory, storage architectures, noise‑reduction techniques, and practical applications such as feature mining, coloring, backend visualization, data analysis, and monitoring for fraud detection in risk control systems.

Data Modelingassociation graphfraud detection

0 likes · 14 min read

Association Graph for Fraud Detection: Theory, Architecture, and Applications

Model Perspective

Oct 26, 2023 · Fundamentals

Modeling Classic Afanti Tales: Donkey, Oil, and Meal Fee Puzzles

This article explores how mathematical modeling and graph‑theoretic methods can rigorously solve three classic Afanti folk stories—dividing donkeys, splitting oil, and a meal‑fee dispute—illustrating the power of formal models for everyday problem solving.

Optimizationfolk talesgraph theory

0 likes · 15 min read

Modeling Classic Afanti Tales: Donkey, Oil, and Meal Fee Puzzles

Model Perspective

Oct 22, 2023 · Fundamentals

How Graph Theory and Complex Networks Shape Everyday Life

Graph theory and complex network principles help model everyday systems—from friendships and city roads to power grids and ecosystems—by representing entities as nodes and relationships as edges, enabling analysis of properties like small‑world effects, clustering, and path lengths to optimize traffic, social insights, and stability.

Power Gridcomplex networksecosystem modeling

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How Graph Theory and Complex Networks Shape Everyday Life

Model Perspective

Sep 1, 2023 · Artificial Intelligence

How to Visualize Neural Networks with Python’s NetworkX: Step‑by‑Step Guide

This tutorial explains how to use the Python library NetworkX to create and visualize simple feed‑forward neural network graphs, covering initialization, node and edge addition, layout customization, and rendering with Matplotlib, plus sample code and example images.

NetworkXNeural Network VisualizationPython

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How to Visualize Neural Networks with Python’s NetworkX: Step‑by‑Step Guide

JD Tech

Jul 24, 2023 · Artificial Intelligence

An Introduction to Graph Computing: Concepts, History, and Real‑World Applications

This article provides a comprehensive overview of graph computing, covering its fundamental concepts, historical development from Euler's bridges to modern graph neural networks, various algorithmic techniques, and practical applications in search, recommendation, finance, fraud detection, and many other AI‑driven domains.

Artificial IntelligenceBig DataGraph Neural Networks

0 likes · 12 min read

An Introduction to Graph Computing: Concepts, History, and Real‑World Applications

Model Perspective

Nov 22, 2022 · Fundamentals

How to Solve the Traveling Salesman Problem Using Python & NetworkX

This article introduces the classic Traveling Salesman Problem, explains its mathematical formulation, discusses its NP‑hard nature, and demonstrates a practical solution in Python by generating random city coordinates, building a distance graph with NetworkX, applying an approximation algorithm, and visualizing the resulting tour.

NP-hardNetworkXOptimization

0 likes · 6 min read

How to Solve the Traveling Salesman Problem Using Python & NetworkX

Model Perspective

Nov 6, 2022 · Operations

Master Evaluation & Optimization Models: Concepts, Methods, and Algorithms

This curated guide compiles recent articles on evaluation and optimization models, covering concepts, preprocessing techniques, weighting methods such as TOPSIS and entropy, as well as linear/integer programming, graph theory, shortest‑path, max‑flow, simulated annealing, and genetic algorithms.

Linear Programmingevaluation modelsgraph theory

0 likes · 6 min read

Master Evaluation & Optimization Models: Concepts, Methods, and Algorithms

Model Perspective

Oct 14, 2022 · Artificial Intelligence

How SimRank Leverages Graph Theory for Powerful Recommendations

SimRank, a graph‑theoretic recommendation algorithm, models users and items as a bipartite graph and computes similarity through iterative matrix operations, with extensions like SimRank++ incorporating edge weights and evidence, while scalable solutions use big‑data frameworks or Monte‑Carlo simulations.

Big DataMatrix ComputationRecommendation systems

0 likes · 8 min read

How SimRank Leverages Graph Theory for Powerful Recommendations

Model Perspective

Sep 17, 2022 · Fundamentals

Why the Seven Bridges of Königsberg Can’t Be Crossed in One Walk – Euler’s Insight

Euler’s classic solution to the Seven Bridges of Königsberg demonstrates how abstracting a real‑world puzzle into a graph reveals that a walk crossing each bridge exactly once is impossible, introducing the Eulerian path theorem that a connected graph is traversable only when it has zero or two odd‑degree vertices.

Eulerian pathKönigsberg bridgesgraph theory

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Why the Seven Bridges of Königsberg Can’t Be Crossed in One Walk – Euler’s Insight

Model Perspective

Jun 27, 2022 · Fundamentals

What Makes a Complex Network Complex? Key Concepts and Characteristics

Complex networks are highly intricate systems characterized by massive node counts, evolving structures, diverse weighted and directed connections, nonlinear dynamics, and heterogeneous node types, and they exhibit hallmark features such as small‑world behavior, clustering, and power‑law degree distributions, all of which are essential for understanding their geometry, formation, evolution, and stability.

complex networksgraph theorynetwork science

0 likes · 5 min read

What Makes a Complex Network Complex? Key Concepts and Characteristics

Model Perspective

Jun 16, 2022 · Fundamentals

Master NetworkX: Install, Build Weighted Graphs, and Find Shortest Paths in Python

This guide walks you through installing NetworkX, creating weighted undirected graphs, visualizing them with various layouts, computing shortest paths using Dijkstra, and generating minimum spanning trees, all with clear Python code examples.

NetworkXPythongraph theory

0 likes · 6 min read

Master NetworkX: Install, Build Weighted Graphs, and Find Shortest Paths in Python

Model Perspective

Jun 7, 2022 · Fundamentals

Understanding Incidence and Adjacency Matrices for Directed and Weighted Graphs

This article explains how to construct incidence and adjacency matrices for both undirected and directed graphs, covering unweighted and weighted cases, and clarifies the matrix entries that indicate edge connections, directionality, and edge weights.

adjacency matrixdirected graphgraph theory

0 likes · 2 min read

Understanding Incidence and Adjacency Matrices for Directed and Weighted Graphs