Graphs and networks

1. Graphs and their spectra

Topics

Eigenvalues of graph Laplacians
curvature of graphs

Jost, Jürgen and Dong Zhang: Cheeger inequalities on simplicial complexes

Mulas, Raffaella ; Horak, Danijela and Jürgen Jost: Graphs, simplicial complexes and hypergraphs : spectral theory and topology

In: Higher-order systems / Federico Battiston... (eds.)

Cham : Springer, 2022. - P. 1-58

(Understanding complex systems)

MIS-Preprint: 17/2022 [DOI]

Jost, Jürgen ; Mulas, Raffaella and Leo Torres: Spectral theory of the non-backtracking Laplacian for graphs

MIS-Preprint: 12/2022 [ARXIV]

Elumalai, Pavithra ; Yadav, Yasharth ; Williams, Nitin ; Saucan, Emil ; Jost, Jürgen and Areejit Samal: Graph Ricci curvatures reveal atypical functional connectivity in autism spectrum disorder

In: Scientific reports, 12 (2022), 8295

MIS-Preprint: 28/2021 [DOI] [ARXIV]

Mulas, Raffaella ; Kuehn, Christian ; Böhle, Tobias and Jürgen Jost: Random walks and Laplacians on hypergraphs : When do they match?

In: Discrete applied mathematics, 317 (2022) 2, p. 26-41

[DOI] [ARXIV]

Barkanass, Vladislav ; Jost, Jürgen and Emil Saucan: Geometric sampling of networks

In: Journal of complex networks, 10 (2022) 4, cnac014

MIS-Preprint: 99/2020 [DOI] [ARXIV]

Jost, Jürgen ; Mulas, Raffaella and Dong Zhang: \(p\)-Laplace operators for oriented hypergraphs

In: Vietnam journal of mathematics, 50 (2022) 2, p. 323-358

[DOI] [ARXIV]

Jost, Jürgen ; Mulas, Raffaella and Florentin Münch: Spectral gap of the largest eigenvalue of the normalized graph Laplacian

In: Communications in mathematics and statistics, 10 (2022) 3, p. 371-381

MIS-Preprint: 6/2020 [DOI] [ARXIV]

Jost, Jürgen ; Mulas, Raffaella and Dong Zhang: Petals and books : the largest Laplacian spectral gap from 1

MIS-Preprint: 23/2021 [ARXIV]

Jost, Jürgen ; Mulas, Raffaella and Dong Zhang: Petals and books : the largest Laplacian spectral gap from 1

MIS-Preprint: 23/2021 [ARXIV]

Jost, Jürgen and Florentin Münch: Characterizations of Forman curvature

[ARXIV]

Jost, Jürgen and Dong Zhang: Discrete-to-continuous extensions : piecewise multilinear extension, min-max theory and spectral theory

[ARXIV]

Jost, Jürgen and Dong Zhang: Discrete-to-continuous extensions, II : Lovász extension, optimizations and eigenvalue problems

[ARXIV]

Jost, Jürgen and Raffaella Mulas: Normalized Laplace operators for hypergraphs with real coefficients

In: Journal of complex networks, 9 (2021) 1, cnab009

[DOI] [ARXIV]

Jost, Jürgen and Raffaella Mulas: Cheeger-like inequalities for the largest eigenvalue of the graph Laplace operator

In: Journal of graph theory, 97 (2021) 3, p. 408-425

MIS-Preprint: 7/2020 [DOI] [ARXIV]

Leal, Wilmer ; Restrepo, Guillermo ; Stadler, Peter F. and Jürgen Jost: Forman-Ricci curvature for hypergraphs

In: Advances in complex systems, 24 (2021) 1, 2150003

[DOI] [ARXIV]

Eidi, Marzieh ; Farzam, Amirhossein ; Leal, Wilmer ; Samal, Areejit and Jürgen Jost: Edge-based analysis of networks : curvatures of graphs and hypergraphs

In: Theory in biosciences, 139 (2020) 4, p. 337-348

MIS-Preprint: 103/2020 [DOI] [ARXIV]

Mulas, Raffaella ; Kuehn, Christian and Jürgen Jost: Coupled dynamics on hypergraphs : master stability of steady states and synchronization

In: Physical review / E, 101 (2020) 6, 062313

[DOI] [ARXIV]

Jost, Jürgen and Dong Zhang: Discrete-to-continuous extensions, I : Lovász extension and Morse theory

MIS-Preprint: 38/2020 [ARXIV]

Jost, Jürgen and Odette Sylvia Yaptieu Djeungue: A generalized discrete Morse-Floer theory

In: Communications in mathematics and statistics, 7 (2019) 3, p. 225-252

[DOI]

Eidi, Marzieh and Jürgen Jost: Ollivier Ricci curvature of directed hypergraphs

In: Scientific reports, 10 (2019) 1, 12466

[DOI] [ARXIV]

Jost, Jürgen ; Rose, Christian and Florentin Münch: Liouville property and non-negative Ollivier curvature on graphs

[ARXIV]

Jost, Jürgen and Raffaella Mulas: Hypergraph Laplace operators for chemical reaction networks

In: Advances in mathematics, 351 (2019), p. 870-896

[DOI] [ARXIV]

Gu, Jiao ; Jost, Jürgen ; Liu, Shiping and Peter F. Stadler: Spectral classes of regular, random, and empirical graphs

In: Linear algebra and its applications, 489 (2016), p. 30-49

[DOI] [ARXIV]

Hua, Bobo and Jürgen Jost: Polynomial growth harmonic functions on groups of polynomial volume growth

In: Mathematische Zeitschrift, 280 (2015) 1-2, p. 551-567

[DOI] [ARXIV]

Hua, Bobo and Jürgen Jost: Lq harmonic functions on graphs

In: Israel journal of mathematics, 202 (2014) 1, p. 475-490

[DOI] [ARXIV]

Bauer, Frank ; Hua, Bobo and Jürgen Jost: The dual Cheeger constant and spectra of infinite graphs

In: Advances in mathematics, 251 (2014), p. 147-194

[DOI] [ARXIV]

Jost, Jürgen and Shiping Liu: Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs

In: Discrete and computational geometry, 51 (2014) 2, p. 300-322

MIS-Preprint: 21/2011 [DOI] [ARXIV]

Bauer, Frank ; Hua, Bobo ; Jost, Jürgen and Shiping Liu: Generalized Ricci curvature and the geometry of graphs

In: Actes des rencontres du CIRM, 3 (2013) 1, p. 69-78

MIS-Preprint: 26/2015 [DOI]

Banerjee, Anirban ; Bauer, Frank and Jürgen Jost: On the spectrum of the normalized Laplacian for directed graphs

Bauer, Frank ; Jost, Jürgen and Anirban Banerjee: Eigenvalues of the normalized graph Laplacian and the architecture of directed networks

Hua, Bobo ; Jost, Jürgen and Xianqing Li-Jost: Polynomial growth harmonic functions on finitely generated abelian groups

In: Annals of global analysis and geometry, 44 (2013) 4, p. 417-432

[DOI] [ARXIV]

Horak, Danijela and Jürgen Jost: Spectra of combinatorial Laplace operators on simplicial complexes

In: Advances in mathematics, 244 (2013), p. 303-336

[DOI] [ARXIV]

Horak, Danijela and Jürgen Jost: Interlacing inequalities for eigenvalues of discrete Laplace operators

In: Annals of global analysis and geometry, 43 (2013) 2, p. 177-207

[DOI] [ARXIV]

Bauer, Frank and Jürgen Jost: Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplace operator

In: Communications in analysis and geometry, 21 (2013) 4, p. 787-845

MIS-Preprint: 30/2010 [DOI] [ARXIV]

Chen, Hao and Jürgen Jost: Minimum vertex covers and the spectrum of the normalized Laplacian on trees

In: Linear algebra and its applications, 437 (2012) 4, p. 1089-1101

[DOI] [ARXIV]

Bauer, Frank ; Jost, Jürgen and Shiping Liu: Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator

In: Mathematical research letters, 19 (2012) 6, p. 1185-1205

MIS-Preprint: 25/2011 [DOI] [ARXIV]

Jost, Jürgen and Hao Chen: Another proof of Oscar Rojo's theorems

[ARXIV]

Banerjee, Anirban and Jürgen Jost: On the spectrum of the normalized graph Laplacian

In: Linear algebra and its applications, 428 (2008) 11-12, p. 3015-3022

[DOI] [ARXIV]

2. Network analysis

Topics

Spectral analysis of networks
distinctive properties of specic classes of networks

Saucan, Emil ; Barkanass, Vladislav and Jürgen Jost: Coarse geometric kernels for networks embedding

In: Information geometry, Vol. not yet known, pp. not yet known

[DOI]

Cohen, Haim ; Nachshon, Yinon ; Maril, Anat ; Naim, Paz M. ; Jost, Jürgen and Emil Saucan: Object-based dynamics : applying Forman-Ricci flow on a multigraph to Assess the Impact of an object on the network structure

In: Axioms, 11 (2022) 9, 486

[DOI]

Cohen, Haim ; Nachshon, Yinon ; Maril, Anat ; Naim, Paz M. ; Jost, Jürgen and Emil Saucan: A path-curvature measure for word-based strategy searches in semantic networks

In: Symmetry, 14 (2022) 8, 1737

[DOI] [FREELINK]

Ravichandran, Janani ; Karthikeyan, Bagavathy Shanmugam ; Jost, Jürgen and Areejit Samal: An atlas of fragrance chemicals in children's products

In: The science of the total environment : an international journal for scientific research into the environment and its relationship with man, 818 (2022), 151682

[DOI]

Böhle, Tobias ; Kuehn, Christian ; Mulas, Raffaella and Jürgen Jost: Coupled hypergraph maps and chaotic cluster synchronization

In: epl, 136 (2022) 4, 4005

[DOI] [ARXIV]

Samal, Areejit ; Pharasi, Hirdesh Kumar ; Ramaia, Sarath Jyotsna ; Kannan, Harish ; Saucan, Emil ; Jost, Jürgen and Anirban Chakraborti: Network geometry and market instability

In: Royal Society Open Science, 8 (2021) 2, 201734

MIS-Preprint: 95/2020 [DOI] [ARXIV]

Leal, Wilmer ; Eidi, Marzieh and Jürgen Jost: Ricci curvature of random and empirical directed hypernetworks

In: Applied network science, 5 (2020), 65

[DOI]

Farzam, Amirhossein ; Samal, Areejit and Jürgen Jost: Degree difference : a simple measure to characterize structural heterogeneity in complex networks

In: Scientific reports, 10 (2020) 1, 21348

MIS-Preprint: 106/2020 [DOI] [ARXIV]

Saucan, Emil ; Samal, Areejit and Jürgen Jost: A simple differential geometry for networks and its generalizations

In: Complex networks and their applications VIII : Volume 1 Proceedings of the eighth international conference on complex networks and their applications ; Complex networks 2019 / Hocine Cherifi... (eds.)

Cham : Springer, 2020. - P. 943-954

(Studies in computational intelligence ; 881)

[DOI] [ARXIV]

Leal, Wilmer ; Eidi, Marzieh and Jürgen Jost: Curvature-based analysis of directed hypernetworks

In: Complex networks 2019 : the 8th international conference on complex networks and their applications ; December 10 - 12, 2019 Lisbon, Portugal ; book of abstract / Hocine Cherifi (ed.)

[s.l.] : International conference on complex networks and their applications, 2019. - P. 32-34

[FREELINK]

Llanos, Eugenio J. ; Leal, Wilmer ; Bernal, Andrés ; Restrepo, Guillermo ; Jost, Jürgen and Peter F. Stadler: A network model of the chemical space provides similarity structure to the system of chemical elements

In: Complex networks 2019 : the 8th international conference on complex networks and their applications ; December 10 - 12, 2019 Lisbon, Portugal ; book of abstract / Hocine Cherifi (ed.)

[s.l.] : International conference on complex networks and their applications, 2019. - P. 308-310

[FREELINK]

Painter, Deryc T. ; Daniels, Bryan C. and Jürgen Jost: Network analysis for the digital humanities : principles, problems, extensions

In: Isis : a journal of the History of Science Society, 110 (2019) 3, p. 538-554

[DOI]

Saucan, Emil ; Sreejith, Remanan P. ; Vivek-Ananth, R. P. ; Jost, Jürgen and Areejit Samal: Discrete Ricci curvatures for directed networks

In: Chaos, solitons and fractals, 118 (2019), p. 347-360

[DOI] [ARXIV]

Weber, Melanie ; Jost, Jürgen and Emil Saucan: Detecting the coarse geometry of networks

MIS-Preprint: 97/2018

Samal, Areejit ; Sreejith, Remanan P. ; Gu, Jiao ; Liu, Shiping ; Saucan, Emil and Jürgen Jost: Comparative analysis of two discretizations of Ricci curvature for complex networks

In: Scientific reports, 8 (2018), 8650

MIS-Preprint: 83/2017 [DOI] [ARXIV]

Saucan, Emil ; Samal, Areejit ; Weber, Melanie and Jürgen Jost: Discrete curvatures and network analysis

In: Match, 80 (2018) 3, p. 605-622

MIS-Preprint: 34/2017 [FREELINK]

Weber, Melanie ; Saucan, Emil and Jürgen Jost: Coarse geometry of evolving networks

In: Journal of complex networks, 6 (2018) 5, p. 706-732

MIS-Preprint: 71/2016 [DOI] [ARXIV]

Weber, Melanie ; Stelzer, Johannes ; Saucan, Emil ; Naitsat, Alexander ; Lohmann, Gabriele and Jürgen Jost: Curvature-based methods for brain network analysis

MIS-Preprint: 51/2017 [ARXIV]

Saucan, Emil and Jürgen Jost: Network topology vs. geometry : from persistent homology to curvature

MIS-Preprint: 5/2017

Sreejith, Remanan P. ; Jost, Jürgen ; Saucan, Emil and Areejit Samal: Systematic evaluation of a new combinatorial curvature for complex networks

In: Chaos, solitons and fractals, 101 (2017), p. 50-67

MIS-Preprint: 67/2016 [DOI] [ARXIV]

Weber, Melanie ; Saucan, Emil and Jürgen Jost: Characterizing complex networks with Forman-Ricci curvature and associated geometric flows

In: Journal of complex networks, 5 (2017) 4, p. 527-550

MIS-Preprint: 56/2016 [DOI] [ARXIV]

Sreejith, Remanan P. ; Jost, Jürgen ; Saucan, Emil and Areejit Samal: Forman curvature for directed networks

MIS-Preprint: 32/2016 [ARXIV]

Weber, Melanie ; Jost, Jürgen and Emil Saucan: Forman-Ricci flow for change detection in large dynamic data sets

In: Axioms, 5 (2016) 4, 26

MIS-Preprint: 30/2016 [DOI] [ARXIV]

Samal, Areejit ; Rodrigues, Joao Matias ; Jost, Jürgen ; Martin, Olivier and Andreas Wagner: Genotype networks in metabolic reaction spaces

In: BMC systems biology, 4 (2010), 30

MIS-Preprint: 12/2010 [DOI]

Banerjee, Anirban and Jürgen Jost: Spectral characterization of network structures and dynamics

In: Dynamics on and of complex networks : applications to biology, computer science, and the social sciences / Niloy Ganguly... (eds.)

Boston, Mass. [u. a.] : Birkhäuser, 2009. - P. 117-132

(Modeling and simulation in science, engineering and technology)

[DOI]

Banerjee, Anirban and Jürgen Jost: Graph spectra as a systematic tool in computational biology

In: Discrete applied mathematics, 157 (2009) 10, p. 2425-2431

[DOI] [ARXIV]

Helbing, Dirk ; Vespignani, Alessando and Jürgen Jost: Preface

In: Networks and heterogeneous media, 3 (2008) 2, i-ii

[DOI]

Banerjee, Anirban and Jürgen Jost: Spectral plot properties : towards a qualitative classification of networks

In: Networks and heterogeneous media, 3 (2008) 2, p. 395-411

[DOI]

Feng, Jian Feng ; Jost, Jürgen and Min Ping Qian (eds.): Networks : from biology to theory

London : Springer, 2007. - XXV, 313 p.

ISBN 978-1-84628-485-4 ISBN 978-1-84628-780-0

[DOI]

TOC

Banerjee, Anirban and Jürgen Jost: Laplacian spectrum and protein-protein interaction networks

[ARXIV]

Banerjee, Anirban and Jürgen Jost: Spectral plots and the representation and interpretation of biological data

In: Theory in biosciences, 126 (2007) 1, p. 15-21

[DOI]

3. Statistical properties

Topics

Motif distributions
random network ensembles
information geometry

Sreejith, Remanan P. ; Mohanraj, Karthikeyan ; Jost, Jürgen ; Saucan, Emil and Areejit Samal: Forman curvature for complex networks

In: Journal of statistical mechanics, 2016 (2016), 063206

MIS-Preprint: 21/2016 [DOI] [ARXIV]

Olbrich, Eckehard ; Kahle, Thomas ; Bertschinger, Nils ; Ay, Nihat and Jürgen Jost: Quantifying structure in networks

In: The European physical journal / B, 77 (2010) 2, p. 239-247

MIS-Preprint: 81/2009 [DOI] [ARXIV]

4. Other

Jost, Jürgen and Guillermo Restrepo: Self reinforcing mechanisms driving the evolution of the chemical space

In: Perspectives on science, Vol. not yet known, pp. not yet known

[FREELINK]

Llanos, Eugenio J. ; Leal, Wilmer ; Bernal, Andrés ; Jost, Jürgen and Peter F. Stadler: Are the chemical families still there? exploration of similarity among elements

[FREELINK]

Teich, Marie ; Leal, Wilmer and Jürgen Jost: Corpus-based metaphor analysis through graph theoretical methods

[ARXIV]

Cohen, Haim ; Nachshon, Yinon ; Naim, Paz M. ; Jost, Jürgen ; Maril, Anat and Emil Saucan: Local detour centrality : a novel local centrality measure for weighted networks

In: Applied network science, 7 (2022), 72

MIS-Preprint: 10/2022 [DOI] [ARXIV]

Wolpert, David ; Price, Michael H. ; Crabtree, Stefani A. ; Kohler, Timothy A. ; Jost, Jürgen ; Evans, James ; Stadler, Peter F. ; Shimao, Hajime and Manfred D. Laubichler: The past as a stochastic process

[ARXIV]

Yamshchikov, Ivan P. ; Nono, Cyrille Merleau ; Samenko, Igor and Jürgen Jost: It means more if it sounds good : yet another hypothesis concerning the evolution of polysemous words

In: Proceedings of the 5th international conference on complexity, future information systems and risk : COMPLEXIS 2020 ; May 8-9, 2020 ; Volume 1 / Reinhold Behringer... (eds.)

Setúbal (Portugal) : SCITEPRESS, 2020. - P. 143-148

MIS-Preprint: 36/2020 [DOI] [ARXIV]

Efer, Thomas ; Heyer, Gerhard and Jürgen Jost: Text Mining am Beispiel der Dramen Shakespeares : Welche neuen Erkenntnisse können moderne formale Methoden liefern?

In: Shakespeare unter den Deutschen : Vorträge des Symposiums vom 15. bis 17. Mai 2014 in der Akademie der Wissenschaften und der Literatur, Mainz / Christa Jansohn... (eds.)

Stuttgart : Franz Steiner, 2015. - P. 217-230

(Abhandlungen der Geistes- und Sozialwissenschaftlichen Klasse ; 2015.2)

MIS-Preprint: 99/2014

Hubicka, Jan ; Jost, Jürgen ; Long, Yangjing ; Stadler, Peter F. and Ling Yang: Relations between graphs

In: Ars mathematica contemporanea, 6 (2013) 2, p. 323-350

MIS-Preprint: 28/2011 [DOI] [ARXIV]

Jost, Jürgen and Leonard Todjihounde: Harmonic nets in metric spaces

In: Pacific journal of mathematics, 231 (2007) 2, p. 437-444

[DOI]

Jost, Jürgen and Maliackal Poulo Joy: Evolving networks with distance preferences

In: Physical review / E, 66 (2002) 3, 036126

MIS-Preprint: 13/2002 [DOI] [ARXIV]

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Graphs and networks

1. Graphs and their spectra

Topics

2. Network analysis

Topics

3. Statistical properties

Topics

4. Other