## Graph Theory

*14 Jul 2015 01:34*

Yet another inadequate place to stash references.

— I mean by this, incidentally, mathematical theory about abstract graphs, which primarily interests me because I want to use them as models of real-world networks...

See also: Graph limits and infinite exchangeable arrays; Graph sampling algorithms; Graph spectra; Network comparsions; Network topology and synchronization

- Recommended, big picture:
- Rick Durrett, Random Graph Dynamics
- M. E. J. Newman, Networks: An Introduction

- Recommended, close-ups:
- Itai Benjamini, Nicolas Curien, "Ergodic Theory on Stationary Random Graphs", arxiv:1011.2526
- Nathan Linial, Eran London and Yuri Rabinovich, "The geometry of graphs and some of its algorithmic applications", Combinatorica
**15**(1995): 215--245 [PDF conference version]

- To read:
- L. Barnett, C. L. Buckley, S. Bullock, "A Graph Theoretic Interpretation of Neural Complexity", arxiv:1011.5334
- Arthur Benjamin, Gary Chartrand and Ping Zhang, The Fascinating World of Graph Theory
- Vincent Blondel, Anahi Gajardo, Maureen Heymans, Pierre Senellart, Paul Van Dooren, "A measure of similarity between graph vertices", cs.IR/0407061
- Fan Chung and Linyuan Lu, Complex Graphs and Networks
- G. R. Grimmett, Probability on Graphs: Random Processes on Graphs and Lattices [Author's book site, including errata and PDF]
- Ben D. MacArthur, Rubén J. Sánchez-García, James
W. Anderson, "On Automorphism Groups of Networks", Discrete
Applied Mathematics
**156**(2008): 3525--3531, arxiv:0705.3215 - Anatolii A. Puhalskii, "Stochastic processes in random graphs", math.PR/0402183 [Large deviations for Erdos-Renyi graphs. Memo to self: how much work would it be to extend this to Markovian graphs?]
- A. Rapoport
- "Contribution to the theory of random and biased
nets", Bulletin of Mathematical Biophysics
**19**(1957): 257--277 - "Cycle distribution in random nets", Bulletin
of Mathematical Biophysics
**10**(1968): 145--157

- "Contribution to the theory of random and biased
nets", Bulletin of Mathematical Biophysics
- Gunther Schmidt, Relational Mathematics
- Nino Shervashidze, Pascal Schweitzer, Erik Jan van Leeuwen, Kurt Mehlhorn, Karsten M. Borgwardt, "Weisfeiler-Lehman Graph Kernels", Journal of Machine Learning Research
**12**(2011): 2539--2561 - R. Solomonoff and A. Rapoport, "Connectivity of Random Nets",
Bulletin of Mathematical Biophysics
**13**(1951): 107--117 [Yes, the R. Solomonoff] - S. V. N. Vishwanathan, Nicol N. Schraudolph, Risi Kondor, Karsten
M. Borgwardt, "Graph
Kernels", Journal
of Machine Learning Research
**11**(2010): 1201--1242 ["Graphs become*ever*so much easier to understand when you project them into a Hilbert space." (Not an actual quote.)]