Graph Theory

This page contains resources about Graph Theory, Complex Networks and Network Science in general.

Subfields and Concepts

 * Undirected Graph
 * Directed Graph
 * Eulerian Path/Cycle
 * Eulerian Graph
 * Hamiltonian Path/Cycle
 * Handshaking Lemma
 * Minimum Spanning Tree
 * Bipartite Graph / Bigraph
 * Topological Metics:
 * Assortativity
 * Betweenness
 * Centrality
 * Closeness
 * Clustering coefficient
 * Degree
 * Degree distribution
 * Geometric measures
 * Network motif
 * Modularity
 * Small-worldnes
 * Link Analysis Algorithms
 * PageRank
 * Hyperlink-Induced Topic Search (HITS) / Hubs and authorities
 * Weisfeiler-Lehman
 * Deep Graphs
 * Complex Networks / Network Science
 * Random Graph
 * Scale-free network
 * Boolean Network (an example of Sequential Dynamical System)
 * Small-World Network
 * Erdos–Renyi Model
 * Barabasi–Albert Model

Video Lectures

 * Graph Theory by Sunil Chandran

Lecture Notes

 * Graph Theory by Christopher Griffin
 * Graph Theory by Paul Johnson
 * Combinatorics: The Fine Art of Counting by Andrew Sutherland
 * Graph Theory by Tero Harju
 * Graph Theory by Maria Axenovich
 * Graphy Theory by Choudum

Books

 * Latora, V., Nicosia, V., & Russo, G. (2017). Complex Networks: Principles, Methods and Applications. Cambridge University Press.
 * Barabasi, A. L. (2016). Network Science. Cambridge University Press.
 * Caldarelli, G., & Catanzaro, M. (2012). Networks: A Very Short Introduction. Oxford University Press.
 * Barrat, A., Barthelemy, M., & Vespignani, A. (2012). Dynamical Processes on Complex Networks. Cambridge University Press.
 * Bona, M. (2011). A Walk Through Combinatorics. 3rd Ed. World Scientific Publishing Company.
 * Estrada, E. (2011). The Structure of Complex Networks: Theory and Applications. Oxford University Press.
 * Xiong, B., & Zheng, Z. (2010). Graph Theory: In Mathematical Olympiad and Competitions (Volume 3). World Scientific.
 * Havlin, S., & Cohen, R. (2010). Complex Networks: Structure, Robustness and Function. Cambridge University Press.
 * Newman, M. (2010). Networks: An Introduction. Oxford University Press.
 * Steen, M. (2010). Graph Theory and Complex Networks: An Introduction, Maarten van Steen.
 * Lewis, T. G. (2009). Network Science: Theory and Applications. John Wiley & Sons.
 * Bondy, J. A., & Murty, U. S. R. (2008). Graph Theory. 3rd Ed. Springer.

Scholarly Articles

 * Watanabe, C., Hiramatsu, K., & Kashino, K. (2018). Understanding Community Structure in Layered Neural Networks. arXiv preprint arXiv:1804.04778.
 * Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D. U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4-5), 175-308.

Software

 * NetworkX - Python

Other Resources

 * What are good books to learn graph theory? - StackExchange
 * What are some good books for self-studying graph theory? - Quora