Graph Theory

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

Subfields and Concepts[edit]

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

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.

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.