Introduction to Algebraic Graph Theory

By Prof. Ranveer Singh | IIT Indore

Learners enrolled: 134

ABOUT THE COURSE:

Algebraic graph theory is the study of graphs (or networks) using linear algebra or matrix theory. This course provides a comprehensive foundation of Algebraic graph theory, areas where graph properties play a critical role include complex network analysis, theoretical computer science, and other related fields. Upon completing the course, learners will acquire the ability to analyze graph properties using matrix theory and related algebraic techniques. They will develop the skills to formulate, derive, and interpret bounds for various graph-theoretic problems. This course is ideal for individuals interested in bridging the gap between theoretical concepts and practical applications in graph analysis.

INTENDED AUDIENCE: Students, Researchers, Professionals

PREREQUISITES: Linear Algebra, Introduction to Graph Theory

INDUSTRY SUPPORT: Microsoft Research, Google, Facebook, LinkedIn and start-ups working in the field of graph.

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	8 weeks
Category :	Computer Science and Engineering
Credit Points :	2
Level :	Undergraduate/Postgraduate
Start Date :	18 Aug 2025
End Date :	10 Oct 2025
Enrollment Ends :	18 Aug 2025
Exam Registration Ends :	29 Aug 2025
Exam Date :	02 Nov 2025 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Graphs, associated matrices and some basic properties, counting number of components, existence of a cycle in a graph, Eigenvalues and eigenvectors

Week 2: Matrix power, spectral theorem, number of walks, closed walks, diameter of graph, counting the number of spanning trees

Week 3: Perron Frobenius theorem for graphs, Rayleigh quotient, minimum eigenvalue, maximum eigenvalue, maximum degree, minimum degree, average degree, Characterization of bipartite graphs

Week 4: Spectrum of induced subgraph, introduction to Cauchy interlacing theorem, proof of Cauchy interlacing theorem

Week 5: Eigenvalues and coloring of graphs, eigenvalues and largest clique, Graphs isomorphism and eigenvalues

Week 6: Graphs determined by eigenvalues, Regular graph, strongly regular graph

Week 7: Friendship theorem, Random walks, Rate of Convergence

Week 8: Algebraic connectivity, Fiedler vector, Introduction to expanders graph

Books and references

C. Godsil and G. Royle, “Algebraic Graph Theory” Springer, 2001.
RB Bapat. “Graphs and Matrices” Springer, 2010.
A. E. Brouwer and W. H. Haemers, Spectra of graphs, Springer, 2011, ISBN: 978-1-4614-1938-9

Instructor bio

Prof. Ranveer Singh

IIT Indore

Dr. Ranveer Singh is an Assistant Professor in the Department of Computer Science and Engineering. He completed his Ph.D. in 2018 and his B.Tech. in 2012 from the Indian Institute of Technology Jodhpur. From December 2017 to October 2019, he was a postdoctoral fellow in the Department of Mathematics at the Technion - Israel Institute of Technology. His research interests are algebraic graph theory and theoretical computer science.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: November 02, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Indore .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

SWAYAM Helpline / Support