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Graphs and Networks

Курс от Birla Institute of Technology & Science, Pilani
Средний≈ 44.2 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Master the mathematical and computational foundations of graph theory and network analysis in this comprehensive course for problem-solvers and analytical thinkers. Explore how graphs model real-world systems—such as social networks, transportation grids, communication systems, and biological pathways. Begin with core concepts like graph properties, connectivity, and planarity, then advance to topics like graph coloring, matching algorithms, network flows, and optimization. Learn to design efficient algorithms, analyze centrality measures, compute maximum flows, and solve minimal cost flow problems. Through mathematical rigor and practical application, you’ll develop both theoretical insight and hands-on problem-solving skills. Applications span scheduling, frequency assignment, image processing, artificial intelligence, and machine learning. Ideal for aspiring researchers, data scientists, and network engineers, this course equips you with essential tools to analyze, optimize, and visualize interconnected systems across diverse domains.

Навыки, которые вы освоите

Graph TheoryNetwork ModelNetwork AnalysisModel OptimizationAlgorithmsGraphingApplied MathematicsArtificial Intelligence and Machine Learning (AI/ML)CombinatoricsImage AnalysisTheoretical Computer ScienceSocial Network AnalysisNetwork EngineeringMathematical ModelingTransportation OperationsEmbeddingsProblem Solving

Программа курса

10 модулей · 209 учебных материалов

01Introduction to Graphs & Networks29 материалов

Course Introduction

Course OverviewЧтениеMeet Your Instructor - Prof. Siddharth GuptaВидеоMeet Your Instructor - Prof. Y V K Ravi KumarВидеоCourse Introductory VideoВидео

Учитесь у экспертов

BITS Pilani Instructors Group

Преподаватель курса

Graphs and Networks
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Обучение на Coursera

≈ 44.2 ч

10 модулей

Язык: Английский

Часть программы вашего университета
Course Structure & Critical InformationЧтение

Why Learn Graphs?

Modeling Real World Networks as GraphsВидеоModeling Real World Networks as GraphsЗаданиеReal World Problems as GraphsВидеоReal World Problems as GraphsЗаданиеRecommended Reading: Why Learn Graphs?Чтение

What are Graphs?

Graphs and Basic DefinitionsВидеоGraphs and Basic DefinitionsЗаданиеDegrees in GraphsВидеоDegrees in GraphsЗаданиеDegree Sequences in GraphsВидеоDegree Sequences in GraphsЗаданиеGraph Sequences and SubgraphsВидеоGraph Sequences and SubgraphsЗаданиеCommon Classes of GraphsВидеоCommon Classes of GraphsЗаданиеDirected GraphВидеоDirected GraphЗаданиеGraph IsomorphismВидеоGraph IsomorphismЗаданиеGraph RepresentationВидеоGraph RepresentationЗаданиеRecommended Reading: What are Graphs?Чтение

Assessment

Let's Practice: Introduction to Graphs & NetworksЗаданиеTest Yourself: Introduction to Graphs & NetworksЗадание
02Connectivity and Reachability29 материалов

Undirected Graph Connectivity

Vertex ConnectivityВидеоVertex ConnectivityЗаданиеEdge ConnectivityВидеоEdge ConnectivityЗаданиеVertex and Edge ConnectivityВидеоVertex and Edge ConnectivityЗаданиеVertex and Edge Connectivity of Cubic GraphsВидеоVertex and Edge Connectivity of Cubic GraphsЗаданиеMenger’s TheoremВидеоMenger’s TheoremЗадание1- and 2- Connected GraphsВидео1- and 2- Connected GraphsЗаданиеBridges and Cut-VerticesВидеоBridges and Cut-VerticesЗаданиеRecommended Reading: Undirected Graph ConnectivityЧтение

Directed Graph Connectivity

Types of ConnectivityВидеоTypes of ConnectivityЗаданиеStrong Directed GraphsВидеоStrong Directed GraphsЗаданиеGraph OrientationВидеоGraph OrientationЗаданиеTournament

Assessment

Network Connectivity AnalysisDIALOGUELet's Practice: Connectivity and ReachabilityЗаданиеTest Yourself: Connectivity and ReachabilityЗадание
03Planar Graphs26 материалов

What is a Planar Graph?

Planar Graphs and DrawingsВидеоPlanar Graphs and DrawingsЗаданиеEuler’s Polyhedral FormulaВидеоEuler’s Polyhedral FormulaЗаданиеProperties of Planar GraphsВидеоProperties of Planar GraphsЗаданиеApplication of Euler’s TheoremВидеоApplication of Euler’s TheoremЗаданиеRecognition of Planar GraphsВидеоRecognition of Planar Graphs ЗаданиеMaximal Planar GraphsВидеоMaximal Planar GraphsЗаданиеOuterplanar GraphsВидеоOuterplanar GraphsЗаданиеRecommended Reading: What is a Planar Graph?Чтение

Dual Graphs

Dual Graph and its PropertiesВидеоDual Graph and its PropertiesЗаданиеSelf-Dual GraphsВидеоSelf-Dual GraphsЗаданиеBipartite Graph and its Dual GraphВидеоBipartite Graph and its Dual GraphЗаданиеPlanarity of Dual Graph

Assessment

Let's Practice: Planar GraphsЗаданиеTest Yourself: Planar GraphsЗадание
04Graph Parameters28 материалов

Colouring, Independent Set & Clique

Vertex ColouringВидеоVertex ColouringЗаданиеTimetable Scheduling Using Vertex ColouringВидеоTimetable Scheduling Using Vertex ColouringЗаданиеIndependent SetВидеоIndependent SetЗаданиеVertex Colouring and Independent SetВидеоVertex Colouring and Independent SetЗаданиеGraphs with Minimum and Maximum Chromatic NumberВидеоGraphs with Minimum and Maximum Chromatic NumberЗаданиеCliqueВидеоCliqueЗаданиеChromatic Number and Clique NumberВидеоChromatic Number and Clique NumberЗаданиеChromatic Number and SubgraphsВидеоChromatic Number and SubgraphsЗаданиеChromatic Number and Maximum DegreeВидеоChromatic Number and Maximum DegreeЗаданиеColoring Planar GraphsВидеоColouring Planar GraphsЗаданиеRecommended Reading: Colouring, Independent Set & CliqueЧтение

Matchings and Domination

MatchingsВидеоMatchingsЗаданиеDominationВидеоDominationЗаданиеRecommended Reading: Matchings and DominationЧтение

Assessment

Let's Practice: Graph ParametersЗаданиеTest Yourself: Graph ParametersЗадание
05Real World Networks14 материалов

Types of Networks

IntroductionВидеоClassification of NetworksВидеоRandom NetworksВидеоScale-Free NetworksВидеоSFN - Mathematical ModelВидеоComparison of ER and BA ModelsВидеоSmall World Networks ВидеоSWN - Mathematical ModelВидеоFew More Types of NetworksВидеоRecommended Reading: Types of NetworksЧтениеTypes of NetworksЗадание

Summary and Assessment

Real-World Network ModelingDIALOGUELet's Practice: Real World NetworksЗаданиеTest Yourself: Real World NetworksЗадание
06Network Analysis Measures15 материалов

Similarity in Networks

IntroductionВидеоSimilarity as a MeasureВидеоStructural SimilarityВидеоRecommended Reading: Similarity in NetworksЧтениеSimilarity in NetworksЗадание

Centrality in Networks

IntroductionВидеоDegree CentralityВидеоBetweenness CentralityВидеоCloseness CentralityВидеоEigen Vector CentralityВидеоEigen Vector Centrality - ExampleВидеоRecommended Reading: Centrality in NetworksЧтениеCentrality in NetworksЗадание

Assessment

Let's Practice: Network Analysis MeasuresЗаданиеTest Yourself: Network Analysis MeasuresЗадание
07Network Flows15 материалов

Flows and Maximal Cost Flows

Flows in a NetworkВидеоFeasible FlowsВидеоFeasible Flows - ExampleВидеоSuper Sources and Super SinksВидеоFord-Fulkerson AlgorithmВидеоFord-Fulkerson Algorithm - ExampleВидеоEdmonds-Karp AlgorithmВидеоEdmonds-Karp Algorithm - ExampleВидеоDinic's AlgorithmВидеоDinic's Algorithm - ExampleВидеоRecommended Reading: Flows and Maximal Cost FlowsЧтениеFlows and Maximal Cost FlowsЗадание

Assessment

Flow Optimization StrategyDIALOGUELet's Practice: Network FlowsЗаданиеTest Yourself: Network FlowsЗадание
08Minimal Cost Flow in a Network 11 материалов

Minimal Cost Flows

IntroductionВидеоSuccessive Shortest Path AlgorithmВидеоCycle – Cancelling AlgorithmВидеоSuccessive Shortest Path Algorithm - ExampleВидеоCycle Cancelling Algorithm - ExampleВидеоNetwork Simplex AlgorithmВидеоLinear Programming (LP) SolverВидеоRecommended Reading: Minimal Cost FlowsЧтениеMinimal Cost FlowsЗадание

Assessment

Let's Practice: Minimal Cost Flow in a Network ЗаданиеTest Yourself: Minimal Cost Flow in a Network Задание
09Matchings in Graphs & Networks18 материалов

Matchings

IntroductionВидеоApplications of MatchingВидеоTypes of MatchingВидеоRecommended Reading: MatchingsЧтениеMatchingsЗадание

Maximum Matchings

Hungarian AlgorithmВидеоHopcroft - Karp AlgorithmВидеоHopcroft - Karp Algorithm - ExampleВидеоBlossom AlgorithmВидеоBlossom Algorithm - ExampleВидеоRecommended Reading: Maximum MatchingsЧтениеMaximum MatchingsЗадание

Other Matchings

Perfect MatchingВидеоMaximum Bipartite MatchingВидеоRecommended Reading: Other MatchingsЧтениеOther MatchingsЗадание

Assessment

Let's Practice: Matchings in Graphs & NetworksЗаданиеTest Yourself: Matchings in Graphs & NetworksЗадание
10Applications of Graphs & Networks24 материалов

Applications

Scheduling TournamentsВидеоScheduling TournamentsЗаданиеDefending the Roman EmpireВидеоDefending the Roman EmpireЗаданиеAssignment of Radio FrequenciesВидеоAssignment of Radio FrequenciesЗаданиеConnected Component LabelingВидеоConnected Component LabelingЗаданиеEconomics and Biological NetworksВидеоEconomics and Biological NetworksЗаданиеTrees in Computer ScienceВидеоTrees in Computer ScienceЗаданиеRecommended Reading: ApplicationsЧтение

Advanced Topics

Computational GeometryВидеоComputational GeometryЗаданиеGraph DrawingВидеоGraph DrawingЗаданиеCombinatorial ReconfigurationВидеоCombinatorial ReconfigurationЗаданиеRecommended Reading: Advanced Topics

Assessment

Graph Theory ApplicationsDIALOGUELet's Practice: Applications of Graphs & NetworksЗаданиеTest Yourself: Applications of Graphs & NetworksЗадание

Course Wrap-Up

Course SummaryЧтение
Видео
TournamentЗадание
Strong TournamentВидео
Strong TournamentЗадание
Recommended Reading: Directed Graph ConnectivityЧтение
Видео
Planarity of Dual GraphЗадание
Recommended Reading: Dual GraphsЧтение
Чтение