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Interesting journal articles, recommended textbooks, and other resources.

Mathematics of Networks: Modulus Theory and Convex Optimization - book

Share useful code snippets, link to external resources, or create dedicated pages for larger scripts and documentation.

The Modulus Book - A collection of modulus-related software tools.

A running list of publications that resulted from the work of NODE group.

On the Sharp Lower Bound for Duality of Modulus., Sylvester Eriksson-Bique and Pietro Poggi-Corradini. Proc. Amer. Math. Soc. 150 (2022), 2955-2968. DOI Arxiv

Fairest edge usage and minimum expected overlap for random trees., Nathan Albin, Jason Clemens, Derek Hoare, Pietro Poggi-Corradini, Brandon Sit, and Sarah Tymochko. Discrete Mathematics. Volume 344, Issue 5 (2021), 112282. DOI Arxiv

New methods for incorporating network cyclic structures to community detection., Behnaz Moradijamei, Heman Shakeri, and Mike Higgins. Physica A: Statistical Mechanics and its Applications, Vol. 561 (2020). DOI Arxiv

Spanning tree modulus for secure broadcast games., Nathan Albin, Kapila Kottegoda, and Pietro Poggi-Corradini. Networks. Vol. 76, n. 3 (2020), Pages 350-365. DOI Arxiv

Designing optimal multiplex networks for certain Laplacian spectral properties., H. Shakeri, A. Tavassoli, E. Ardjmand, and Pietro Poggi-Corradini. Physical Review E, Vol 102, n. 2 (2020). DOI Arxiv

The Rickman-Picard Theorem., Mario Bonk and Pietro Poggi-Corradini. Annales Acad. Sci. Fennicae 44 (2019), 615-633. DOI Arxiv

Modulus metrics on networks., Nathan Albin, Nethali Fernando, and Pietro Poggi-Corradini. Discrete & Continuous Dynamical Systems - B 24(1), 24 (2019). DOI

Blocking duality for p-modulus on networks and applications., Nathan Albin, Jason Clemens, Nethali Fernando, and Pietro Poggi-Corradini. Annali di Matematica Pura ed Applicata (1923-) 198(3), November (2018), 973–999. DOI Arxiv

Infinity modulus and the essential metric., Nathan Albin, Jared Hoppis, Pietro Poggi-Corradini, and Nageswari Shanmugalingam. Journal of Mathematical Analysis and Applications 467(1), 46 (2018) 570–584. DOI Arxiv

Generalization of effective conductance centrality for egonetworks., Heman Shakeri, Behnaz Moradi-Jamei, Pietro Poggi-Corradini, Nathan Albin, and Caterina Scoglio. Physica A: Statistical Mechanics and its Applications, 511 (2018). DOI Arxiv

Network clustering and community detection using modulus of families of loops., Heman Shakeri, Pietro Poggi-Corradini, Nathan Albin, and Caterina Scoglio. Phys. Rev. E, January 95 (2017), 012316. DOI Arxiv

Open problems and new directions for p-modulus on networks., Nathan Albin and Pietro Poggi-Corradini. Geometric Function Theory in Higher Dimension, (2017), 129. DOI

Modulus of families of walks on graphs., Nathan Albin, Pietro Poggi-Corradini, Faryad Darabi Sahneh, and M. Goering. Proceedings of Complex Analysis and Dynamical Systems VII (Contemporary Mathematics), 699 (2017), 35–56. Arxiv

Maximizing algebraic connectivity in interconnected networks., H. Shakeri, N. Albin, F. Sahneh, P. Poggi-Corradini, and C. Scoglio. Physical Review E, March 93 (2016), 030301. DOI Arxiv

Minimal subfamilies and the probabilistic interpretation for modulus on graphs., N. Albin and P. Poggi-Corradini. Journal of Analysis, (2016), 1–26. DOI Arxiv

Generalized network measures based on modulus of families of walks., H. Shakeri, P. Poggi-Corradini, C. Scoglio, and N. Albin. Journal of Computational and Applied Mathematics, 307 (2016) 316-318. DOI

Numerical Investigation of Metrics for Epidemic Processes on Networks., M. Goering, N. Albin, F. Sahneh, C. Scoglio, and P. Poggi-Corradini. 2015 49th Asilomar Conference on Signals, Systems and Computers, November (2015), 1317–1322. DOI Arxiv

Modulus on graphs as a generalization of standard graph theoretic quantities., Nathan Albin, Megan Brunner, Roberto Perez, Pietro Poggi-Corradini, and Natalie Wiens. Conformal Geometry and Dynamics, 19 (2015), 298–317. DOI Arxiv

Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks., Heman Shakeri, Faryad Darabi Sahneh, Caterina Scoglio, Pietro Poggi-Corradini, and Victor M. Preciado. Math. Biosci. Eng. 12(3), 12 (2015), 609–623. DOI

Effective resistance on graphs and the epidemic quasimetric., J. Ericson, P. Poggi-Corradini, and H. Zhang. Involve 7(1), 7 (2014), 97–124.