MIT OpenCourseWare

Browse materialsMIT 1.022 · Fall 2018

Introduction to Network Models

Art: AmCyc Bridge - New York and Brooklyn Suspension Bridge, published… · Public domain

Instructor: Dr. Amir Ajorlou
Term: Fall 2018
Level: Undergraduate
What's inside: 1 lecture note · 1 reading · 35 other files · 7 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 1.022 Introduction to Network Models, Fall 2018, Dr. Amir Ajorlou — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Lecture Notes

18 files

Assignments

11 files

Final Project

Controlling Epidemics on Networks

Related Resources

MIT OpenCourseWare, Dr. Amir Ajorlou, 1.022 Introduction to Network Models, Fall 2018.

License: CC BY-NC-SA 4.0 · Edition: Fall 2018 · Open the original course on OCW ↗

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Introduction to Network Models

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Final Project

Controlling Epidemics on Networks

Related Resources

Lecture 2: Introduction to graph theory More on graph theory: Connectivity, components, giant components, distance, small-world phenomenon, adjacency and incidence matrices.

Lecture 3: Strong and weak ties, triadic closure, and homophily Homework 1 distributed

Lecture 4: Centrality measures Detection and identi cation of important agents. Degree, closeness, betweenness, eigenvector, and Katz centrality.

Lecture 5: Centrality and web search, spectral graph theory Page rank and web search. Eigenvalues and eigenvectors of graph matrices and their properties. Quadratic forms on graphs and Laplacian.

Lecture 11: Con figuration model and small-world graphs Con guration model, emergence of the giant component. Small-world graphs: De nition from rewiring a regular graph, balance between clustering coefficient and network diameter.

Lecture 12: Growing networks Growing networks. Preferential attachment and power laws: the rich get richer effect. Degree distribution observed in real life, example of a dynamic generative process leading to this distribution, mean fi eld analysis.

Lecture 15: Markov chains Perron-Frobenius theorem. Random walk on graphs.

Lecture 20: Epidemics Models of diffusion without network structure: Bass model Models of diffusion with network structure The SIR Epidemic Model The SIS Epidemic Model

Lecture 23: Application of game theory to networks Traffic equilibrium: non-atomic traffic models. Braess’s Paradox. Socially-Optimal routing and inefficiency of equilibrium. Homework 8 distributed

Lecture 24: Course review and discussion

Lecture 25: Project presentations