reading.md

In 2020, I was thinking about this problem and before I fully understood the pattern I was seeing I ran across a few papers that inspired me:

• Plessas, D. J. (2011). The categories of graphs. University of Montana.
• McRae, G., Plessas, D., & Rafferty, L. (2012). On the Concrete Categories of Graphs. arXiv preprint arXiv:1211.6715.

Simplical Sets, Nerves, etc. Easy Overview

• Milewski, B. (2018) Keep it Simplex, Stupid! Bartosz Milewski's Programming Cafe. 11 December.
• Friedman, G. (2008). An elementary illustrated introduction to simplicial sets. arXiv preprint arXiv:0809.4221.
• Riehl, E. (2011). A leisurely introduction to simplicial sets. Unpublished expository article available online at http://www.math.harvard.edu/~eriehl.

Jump Right In

• Eilenberg, S., & Zilber, J. A. (1950). Semi-simplicial complexes and singular homology. Annals of Mathematics, 499-513.
• Segal, G. (1968). Classifying spaces and spectral sequences. Publications Mathématiques de l'IHÉS, 34, 105-112.
• Segal, G. (1974). Appendix A. Categories and cohomology theories. Topology, 13(3), 293-312.
• May, J. P. (1992). Simplicial Objects in Algebraic Topology. United Kingdom: University of Chicago Press.
• Rezk, C., Schwede, S., & Shipley, B. (2001). Simplicial structures on model categories and functors. American Journal of Mathematics, 123(3), 551-575.
• Goerss, P. G., & Hopkins, M. J. (2003). Moduli spaces of commutative ring spectra. Preprint.
• Blanc, D., Dwyer, W. G., & Goerss, P. G. (2004). The realization space of a Π-algebra: a moduli problem in algebraic topology. Topology, 43(4), 857-892.
• Weber, M. (2007). Familial 2-functors and parametric right adjoints. Theory Appl. Categ, 18(22), 665-732.
• Moerdijk, I., & Weiss, I. (2007). Dendroidal sets. Algebraic & Geometric Topology, 7(3), 1441-1470.
• Allegretti, D. G. (2008). Simplicial Sets and van Kampen’s Theorem. Preprint.
• Gelfand, S. I., Manin, Y. I. (2013). Methods of Homological Algebra. Germany: Springer Berlin Heidelberg.

Simplical Sets and Graphs

• Jonsson, J. (2005). Simplicial complexes of graphs (pp. 0283-0283). Kungl. Telniska högskolan.
• Pal, S. P. (2007). Hypergraphs, Simplicial Complexes and Geometric Graphs CS60035: Special Topics on Algorithms Autumn 2007.
• Spivak, D. I. (2009). Higher-dimensional models of networks. arXiv preprint arXiv:0909.4314.
• Martino, A., & Rizzi, A. (2020). (Hyper) graph kernels over simplicial complexes. Entropy, 22(10), 1155.

Dedekind Cuts, Dedekind Completions

• nLab. Dedekind cut.
• nLab. Dedekind completion.
• Fornasiero, A., & Mamino, M. (2008). Arithmetic of Dedekind cuts of ordered Abelian groups. Annals of Pure and Applied Logic, 156(2-3), 210-244.

Hypergraphs

• Gallo, G., Longo, G., Pallottino, S., & Nguyen, S. (1993). Directed hypergraphs and applications. Discrete applied mathematics, 42(2-3), 177-201.
• Klamt S, Haus U-U, Theis F (2009) Hypergraphs and Cellular Networks. PLoS Comput Biol 5(5): e1000385. https://doi.org/10.1371/journal.pcbi.1000385
• Thakur, M., & Tripathi, R. (2009). Linear connectivity problems in directed hypergraphs. Theoretical Computer Science, 410(27-29), 2592-2618.
• Galeana-Sánchez, H., & Manrique, M. (2009). Directed hypergraphs: A tool for researching digraphs and hypergraphs. Discussiones Mathematicae Graph Theory, 29(2), 313-335.
• Butts, C. T. (2010). A note on generalized edges.
• Gao, Y., Wang, M., Zha, Z. J., Shen, J., Li, X., & Wu, X. (2012). Visual-textual joint relevance learning for tag-based social image search. IEEE Transactions on Image Processing, 22(1), 363-376.
• Javaid, I., Haider, A., Salman, M., & Mehtab, S. (2014). Resolvability in Hypergraphs. arXiv preprint arXiv:1408.5513.
• Ritz, A., Tegge, A. N., Kim, H., Poirel, C. L., & Murali, T. M. (2014). Signaling hypergraphs. Trends in biotechnology, 32(7), 356-362.
• Ritz, A., Avent, B., & Murali, T. M. (2015). Pathway analysis with signaling hypergraphs. IEEE/ACM transactions on computational biology and bioinformatics, 14(5), 1042-1055.
• Ausiello, G., & Laura, L. (2017). Directed hypergraphs: Introduction and fundamental algorithms---a survey. Theoretical Computer Science, 658, 293-306.
• Kamiński B, Poulin V, Prałat P, Szufel P, Théberge F (2019) Clustering via hypergraph modularity. PLoS ONE 14(11): e0224307. https://doi.org/10.1371/journal.pone.0224307
• Vieira, L. S., & Vera-Licona, P. (2019). Computing Signal Transduction in Signaling Networks modeled as Boolean Networks, Petri Nets, and Hypergraphs. bioRxiv, 272344.
• Vieira, L. S., & Vera-Licona, P. (2019). Supplementary Information: Computing Signal Transduction in Signaling Networks modeled as Boolean Networks, Petri Nets, and Hypergraphs. bioRxiv, 272344.
• Franzese N, Groce A, Murali TM, Ritz A (2019) Hypergraph-based connectivity measures for signaling pathway topologies. PLoS Comput Biol 15(10): e1007384. https://doi.org/10.1371/journal.pcbi.1007384
• Presentation Board. Franzese N, Groce A, Murali TM, Ritz A (2019) Hypergraph-based connectivity measures for signaling pathway topologies. PLoS Comput Biol 15(10): e1007384.
• Eidi, M., & Jost, J. (2020). Ollivier ricci curvature of directed hypergraphs. Scientific Reports, 10(1), 1-14.
• Do, M. T., Yoon, S. E., Hooi, B., & Shin, K. (2020, August). Structural patterns and generative models of real-world hypergraphs. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (pp. 176-186).
• Lee, G., Choe, M., & Shin, K. (2021, April). How Do Hyperedges Overlap in Real-World Hypergraphs?-Patterns, Measures, and Generators. In Proceedings of the Web Conference 2021 (pp. 3396-3407).

Papers Mentioning Hyperloops

• Pearson, K. J. (2015). Spectral hypergraph theory of the adjacency hypermatrix and matroids. Linear Algebra and its Applications, 465, 176-187.
• Leal, W., Eidi, M., & Jost, J. (2020). Ricci curvature of random and empirical directed hypernetworks. Applied network science, 5(1), 1-14.
• Surana, A., Chen, C., & Rajapakse, I. (2021). Hypergraph dissimilarity measures. arXiv preprint arXiv:2106.08206.

Paths and Category Theory

• Jardine, J. F. (2006). Categorical homotopy theory. Homology, Homotopy and Applications, 8(1), 71-144.
• Joyal, A. (2008). Notes on quasi-categories. preprint.
• Jardine, J. F. (2010). Path categories and resolutions. Homology, Homotopy and Applications, 12(2), 231-244.
• Jardine, J. F. (2019). Path categories and quasi-categories. arXiv preprint arXiv:1909.08419.
• Jardine, J. F. (2019). Complexity reduction for path categories. arXiv preprint arXiv:1909.08433.
• Jardine, J. F. (2019). Data and homotopy types. arXiv preprint arXiv:1908.06323.

Hyperpaths

• Nguyen, S., & Pallottino, S. (1989). Hyperpaths and shortest hyperpaths. In Combinatorial Optimization (pp. 258-271). Springer, Berlin, Heidelberg.
• Nguyen, S., Pallottino, S., & Gendreau, M. (1998). Implicit enumeration of hyperpaths in a logit model for transit networks. Transportation Science, 32(1), 54-64.
• Marcotte, P., & Nguyen, S. (1998). Hyperpath formulations of traffic assignment problems. In Equilibrium and advanced transportation modelling (pp. 175-200). Springer, Boston, MA.
• Nielsen, L. R., Pretolani, D., & Andersen, K. (2001). A remark on the definition of a B-hyperpath. Technical report, Department of Operations Research, University of Aarhus.
• Lozano, A., & Storchi, G. (2002). Shortest viable hyperpath in multimodal networks. Transportation Research Part B: Methodological, 36(10), 853-874.
• Nielsen, L. R., Andersen, K. A., & Pretolani, D. (2005). Finding the K shortest hyperpaths. Computers & operations research, 32(6), 1477-1497.
• Noh, H., Hickman, M., & Khani, A. (2012). Hyperpaths in network based on transit schedules. Transportation research record, 2284(1), 29-39.
• Khani, A., Hickman, M., & Noh, H. (2015). Trip-based path algorithms using the transit network hierarchy. Networks and Spatial Economics, 15(3), 635-653.
• Xu, Z., Xie, J., Liu, X., & Nie, Y. M. (2020). Hyperpath-based algorithms for the transit equilibrium assignment problem. Transportation Research Part E: Logistics and Transportation Review, 143, 102102.
• Miller, J., Nie, Y., & Liu, X. (2020). Hyperpath truck routing in an online freight exchange platform. Transportation Science, 54(6), 1676-1696.
• Dahari, A., & Linial, N. (2020). Hyperpaths. arXiv preprint arXiv:2011.09936.
• Krieger, S., Kececioglu, J. (2021) Approaches for shortest hyperpath and minimum-hyperedge factories in directed hypergraphs
• What is a hyperpath, anyway?

Category theoretic papers on open graphs

• Dixon, L., & Kissinger, A. (2013). Open-graphs and monoidal theories. Mathematical Structures in Computer Science, 23(2), 308-359.
• Kissinger, A. (2014). Finite matrices are complete for (dagger-) hypergraph categories. arXiv preprint arXiv:1406.5942.
• Fong, B. (2015). Decorated cospans. arXiv preprint arXiv:1502.00872.
• Fong, B. (2016). The algebra of open and interconnected systems. arXiv preprint arXiv:1609.05382.
• Bonchi, F., Seeber, J., & Sobocinski, P. (2018). Graphical conjunctive queries. arXiv preprint arXiv:1804.07626. Proudfoot, N., & Ramos, E. (2019). The contraction category of graphs. arXiv preprint arXiv:1907.11234.
• Jenča, G. (2019). Two monads on the category of graphs. Mathematica Slovaca, 69(2), 257-266.
• Master, J. (2020). The open algebraic path problem. arXiv preprint arXiv:2005.06682.
• Patterson, E., Lynch, O., & Fairbanks, J. (2021). Categorical Data Structures for Technical Computing. arXiv preprint arXiv:2106.04703.
• Patterson, E., Lynch, O., & Fairbanks, J. (2021). Categorical Data Structures for Technical Computing. arXiv preprint arXiv:2106.04703.
• Chih, T., & Scull, L. (2021). A homotopy category for graphs. Journal of Algebraic Combinatorics, 53(4), 1231-1251.
• Hackney, P. (2021). Categories of graphs for operadic structures. arXiv preprint arXiv:2109.06231.
• Bumpus, B. M., & Kocsis, Z. A. (2021). Spined categories: generalizing tree-width beyond graphs. arXiv preprint arXiv:2104.01841.
• Master, J. E. (2021). Composing Behaviors of Networks. University of California, Riverside.
• networks_robotics_web.pdf

Introductory Books

• Deo, N. (1974). Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation).
• Chartrand, G. (1977). Introductory graph theory. Courier Corporation.
• Biggs, N., Lloyd, E. K., Wilson, R. J. (1986). Graph theory, 1736-1936. United Kingdom: Clarendon Press.
• Biggs, N. L. (1993). Algebraic graph theory (No. 67). Cambridge university press.
• Tutte, W.T. (2001). Graph Theory. Cambridge University Press, p. 30, ISBN 978-0-521-79489-3
• Bender, E.A. & Williamson, S.G. (2010) Lists, Decisions and Graphs.
• Kepner, J., & Gilbert, J. (Eds.). (2011). Graph algorithms in the language of linear algebra. Society for Industrial and Applied Mathematics.

Linear algebra

• Kepner, J., Aaltonen, P., Bader, D., Buluç, A., Franchetti, F., Gilbert, J., ... & Moreira, J. (2016, September). Mathematical foundations of the GraphBLAS. In 2016 IEEE High Performance Extreme Computing Conference (HPEC) (pp. 1-9). IEEE.
• Gilbert, J. (2018) Graph Algorithms in the Language of Linear Algebra: How did we get here, where do we go next? IPDPS Graph Algorithms Building Blocks. [Presentation Slides]