Mathematical Technology of Networks

Book Preface

(Center for interdisciplinary Research) in Bielefeld, Germany and saw the participation of almost 50 researchers from four continents.

This conference has brought together functional analysts, mathematical physicists and graph theorists as well as natural scientists using networks as a tool in their own research field—most notably, in selected areas of neuroscience and machine learning. The topics treated during the meeting dwelt on functional analytical, probabilistic and spectral aspects in the study of graphs, quantum graphs and complex networks.

I gratefully acknowledge the financial and logistic support of the ZiF, which made the conference possible in the framework of my fellowship of the Young ZiF. These proceedings do succeed in mirroring the variety of scientific background of the conference participants and in giving a hint of how broad the topic of networks, graphs and their applications currently is. Considering its decennial experience in scientific bridge-building, the ZiF was certainly just the perfect stage for this meeting.

Special thanks are due to the whole staff of the ZiF and in particular to the executive secretary Britta Padberg and to Trixi Valentin of the conference office, for their constant support and their assistance as the conference was organised and then carried out. With their aid several minor organisational problems and even the outgrowth of a hurricane warning could be defused.

Last but not least, let me thank all the contributors and all the referees. Proceedings article seems to be little fashionable in the current mathematical demimonde: It is all the more remarkable that so many quality research and survey articles have been written with enthusiasm and then competently evaluated for this volume.

Contents

Lack of Ground State for NLSE on Bridge-Type Graphs . . . . . . . . . . . . . . . . . . . 1
Riccardo Adami, Enrico Serra, and Paolo Tilli Instability of Stationary Solutions of Evolution Equations on Graphs Under Dynamical Node Transition . . . 13
Joachim von Below and Baptiste Vasseur Statistical Characterization of a SmallWorld Network Applied to Forest Fires . . 27
Fatima Zahra Benzahra Belkacem, Noureddine Zekri, and Mekki Terbeche Network Dynamics as an Inverse Problem . . . . . 39
Jose Casadiego and Marc Timme Dynamics on a Graph as the Limit of the Dynamics on a “Fat Graph”. . . 49
Gianfausto Dell’Antonio and Alessandro Michelangeli Spectral Inequalities for Quantum Graphs .  . . . . 65
Semra Demirel-Frank Intrinsic Metrics on Graphs: A Survey . .  . 81
Matthias Keller Spectral Gap for Complete Graphs: Upper and Lower Estimates . . . . 121
Pavel Kurasov Sharp Spectral Estimates for Periodic Matrix-Valued Jacobi Operators . .  133

Identifying Key Nodes in Social Networks UsingMulti-Criteria Decision-Making Tools . .. . . . . . 137
Iman Mesgari, Mehrdad Agha Mohammad Ali Kermani, Robert Hanneman, and Alireza Aliahmadi On Band-Gap Structure of Spectrum in Network Double-Porosity Models . . . . 151
Svetlana E. Pastukhova Spectra, Energy and Laplacian Energy of Strong Double Graphs . . . . . 175
Shariefuddin Pirzada and Hilal A. Ganie System/Environment Duality of Nonequilibrium Network Observables .. . . . 191
Matteo Polettini