Professor Shlomo Havlin
Introduction to Networks of Networks
Jianxi Gao, Amir Bashan, Louis Shekhtman and Shlomo Havlin.
IOP Publishing, 2022
The essence of network science is the realization that the behavior of many complex systems in nature and technology cannot be understood only by analyzing their components. Rather, the interactions between the components, considered as a network usually, play a critical role in the functioning of the system. Network science, initiated around the year 2000, has successfully formulated methodological frameworks and scientific tools to study complex systems composed of many interacting elements, leading to a deep and detailed understanding of their structural and functional fundamental features. A decade later, in 2010, scientists from diverse fields started to develop mathematical frameworks and study more complex scenarios where the networks themselves are interconnected and dependent on each other, forming networks of networks. These systems have also been referred to as interdependent networks, multilayer networks, multiplex networks or multi-dimensional networks.
In this book, we introduce the basic concepts and tools in the developing field of networks of networks, reviewing their fundamental features and new properties, while focusing especially on interdependent networks, which are unique since the interactions between the networks (dependency links) are different from the interactions within the networks (connectivity links). The book is intended both for readers who want a broad overview of the field as well as to those who are interested in a deeper exploration of the methods and applications of this new paradigm.
Percolation in Spatial Networks
B. Gross and S. Havlin
Cambridge University Press, 2022
Percolation theory is a well studied process utilized by networks theory to understand the resilience of networks under random or targeted attacks. Despite their importance, spatial networks have been less studied under the percolation process compared to the extensively studied non-spatial networks. In this Element, the authors will discuss the developments and challenges in the study of percolation in spatial networks ranging from the classical nearest neighbors lattice structures, through more generalized spatial structures such as networks with a distribution of edge lengths or community structure, and up to spatial networks of networks.
Fractals and Disordered Systems
Editors: A Bunde and S. Havlin
Second edition 1992;
Revised and Enlarged edition 1996.
Armin Bunde,University of Giessen, Germany
and Shlomo Havlin,Bar Ilan University, Ramat-Gan, Israel (eds.)
Second Revised and Enlarged Edition
Fractals and disordered systems have recently become a focus of great interest in research.
This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools for describing them in mathematical language.
A substantial part of this book is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research.
In each chapter, the connection between theory and experiment is emphasized. This book also includes a special chapter on “Fractals and Experiments” where experimental studies of fractal systems are presented. The fully revised second edition of Fractals and disordered systems includes updated literature in this important field. It is pedagogically written and will be also useful for students, teachers, and active scientists who want to become familiar with this fascinating subject.
1. Fractals and Multifractals: The Interplay of Physics and Geometry(H. E. Stanley).
2. Percolation I (A. Bunde and S. Havlin).
3. Percolation II (S. Havlin and A. Bunde)
4. Fractal Growth (A. Aharony).
5. Fractures (H. J. Herrmann).
6. Transport Across Irregular Interfaces: Fractal Electrodes, Membranes and Catalysts (B. Sapoval).
7. Fractal Surfaces and Interfaces (J. F. Gouyet, M. Rosso and B. Sapoval).
8. Fractals and Experiments (J. Kjems).
9. Cellular Automata (D. Stauffer).
10. Exactly Self-similar Left-sided Multifractals (B. B. Mandelbrot and Carl J. G. Evertsz with new Appendices B and C by R. H. Riedi, B. B. Mandelbrot).
Fractals in Science
Editors: A Bunde and S. Havlin
Second edition 1995
Armin Bunde, University of Giessen, Germany.
and Shlomo Havlin,Bar Ilan University, Ramat-Gan, Israel (eds.)
This book presents a comprehensive study of how the unifying topic of irregular complex systems can be used to analyze structure and processes across the field of the natural sciences, including chemistry, biology,geophysics, physics, and medicine. It also gives an introduction to fractal geometry and discusses in great detail fractals in biology, self-organized criticality, rough surfaces and interfaces, random walks, chemical reactions, and fractals in chemistry , biology, and medicine. A separate chapter (Computer Exploration of Fractals, Chaos and Cooperativity) includes the 14 interactive programs on the accompanying 3 1/2 inch diskette that enable readers to simulate the geometry and behavior of systems in diverse areas of natural science.
1.A Brief Introduction to Fractal Geometry (A. Bunde and S. Havlin).
2.Fractals and Self-Organized Criticality (P. Bak and M. Creutz).
3.Fractals in Biology and Medicine: From DNA to the Heartbeat
(S. V. Buldyrev, A. L. Golodberger, S. Havlin, C.-K. Peng, and H. E. Stanley).
4.Self-affine Interfaces (J. Kertesz and T. Vicsek).
5.A Primer for Random Walkology(G. H. Weiss).
6.Polymers (M. Daoud).
7.Kinetics and Spatial Organizations of Competitive Reactions(S. Redner and F. Leyvraz).
8.Fractal Analysis in Heterogeneous Chemistry (D. Avnir, R. Gutfraind and D. Farin).
9.Computer Exploration of Fractals, Chaos and Cooperativity (D. C. Rapaport and M. Meyer).
Diffusion and Reactions in Fractals and Disordered Systems
D. Ben-Avraham and S. Havlin
Cambridge University Press, 2000
Daniel ben-Avraham, Clarkson University, New York, U.S.A.
and Shlomo Havlin, Bar Ilan University, Ramat-Gan, Israel (eds.)
Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far-reaching implications for a host of phenomena.
This book describes diffusion and transport in disordered media such as fractals, porous rocks, and random resistor networks.
Part one contains material of general interest to statistical physics:fractals,percolation theory, regular random walks and diffusion,continuous-time random walks and Levy walks and flights.
Part two covers anomalous diffusion in fractals and disordered media,while Part three serves as an introduction to the kinetics of diffusion-limited reactions.
Part four discusses the problem of diffusion-limited coalescence in one dimension. This book, written in a pedagogical style,is intended for upper-level undergraduates and graduate students studying physics, chemistry, and engineering. It also will be of particular interest to young researchers requiring a clear introduction to the field.
Part one: Basic concepts
3.Random walks and diffusion
4.Beyond random walks
Part two: Anomalous diffusion
5.Diffusion in the Sierpinski gasket
6.Diffusion in percolation clusters
7.Diffusion in loopless structures
8.Disordered transition rates
9.Biased anomalous diffusion
Part three: Diffusion-limited reactions
11.Classical models of reactions
13.Simple reaction models
Part four: Diffusion-limited coalescence: an exactly solvable model
15.Coalescence and the IPDF method
18.Complete representations of coalescence
19.Finite reaction rates
Appendix A The fractal dimension
Appendix B The number of distinct sites visited by random walks
Appendix C Exact enumeration
Appendix D Long-range correlationss
Focus on Complex Networked Systems: Theory and Application
Issue: Volume 9, June 2007
Journal: New Journal of Physics
Editors: Shlomo Havlin, Maziar Nekovee and Yamir Moreno
Complex networks are becoming manifest in many fields of contemporary science, including mathematics, physics, computer science, biology, engineering, social sciences and economics. As part of a broad movement towards research in complex systems, scientists have recently found a striking degree of self-organization that emerges in networks representing seemingly diverse complex systems (Barabasi A L 2005 Nat. Phys. 1 68). The research subject of complex networks comprises the study of how networks emerge and evolve, what is their topology, how robust they are, what new phenomena emerge as a result of the interplay between the structure and dynamics and how can we take advantage of this knowledge for applications in a wide range of natural and man-made systems.
The challenge is to understand and accurately model the structure of complex networks to get more insight and a better understanding of their complex topology and functional behavior, since both are intimately linked. This makes the network approach particularly suitable to explore important aspects of complexity.
The last decade has witnessed a burst of research activity in the study of large systems made of many non-identical entities, whose interaction or interconnection patterns show complex network-like structures. The research community has benefited from the massive and comparative analysis of networks from different fields, which has produced a series of unexpected results and has shown that previous models proposed in mathematical graph theory are very far from reality (see e.g., Newman M E J 2003 SIAM Rev. 45 167, Boccaletti S et al 2006 Phys. Rep. 424 175).
Broadly speaking, research on such complex networks has found its focus in several directions. The first direction of research deals with the structure of networks and consists of identifying the unifying principles and statistical properties that are common to most real networks and how these can be captured via network generation models and algorithms. Another important body of work deals with spreading and percolation-like processes in complex networks, addressing a variety of phenomena ranging from disease spreading to information flow and resilience to random failures and attacks.
A third and promising branch of research has arisen in the last few years spurred by the new insights gained through network modeling. It has to do with the study of the behavior of large assemblies of dynamical and nonlinear systems interacting via complex topologies. Phenomena such as synchronization, the emergence of cooperation in social and biological systems, as well as signaling and gene regulatory dynamics and other biochemical processes are now being tackled with a fresh viewpoint by considering both sources of entangled complexity: the structure and the dynamics of the system’s constituents. Finally, due to adaptive and dynamical wiring, networks are also dynamical entities, whose topologies evolve and adapt in time. This is another field of research which is just emerging with promising applications to a number of areas including wireless communication systems and brain dynamics.
Though modern network theory has produced a number of relevant results in the last few years, it is still at an early stage, particularly when it comes to applications in real systems and to the comprehension of the relation between their structure and function (dynamics).
The subject of complex networks is highly interdisciplinary and physicists are making important contributions to the theory, with applications to areas as diverse as computer science, mathematical epidemiology, social and biological sciences, etc. This spirit is reflected in the present issue, which has collected contributions from scientists at the very forefront of the theory and applications of complex networks.
The articles that make up this Focus Issue are only examples of the wide range of topics that are explored using the tools developed during the last few years. Although important progress has been made during the last decade, our understanding of complex networked systems, their structure and dynamics, is still far from well-established. We hope that this Focus Issue will further contribute towards better understanding of complex systems.
The articles below represent the first contributions and further additions will appear.
- Beyond centrality classifying topological significance using backup efficiency and alternative paths
Yuval Shavitt and Yaron Singer
- Scatter networks: a new approach for analysing information scatter
Lada A Adamic, K Suresh and Xiaolin Shi
- New approaches to model and study social networks
P G Lind and H J Herrmann
- Search in spatial scale-free networks
H P Thadakamalla, R Albert and S R T Kumara
- Worm epidemics in wireless ad hoc networks
- A measure of centrality based on network efficiency
V Latora and M Marchiori
- Dynamical and spectral properties of complex networks
Juan A Almendral and Albert Di’az-Guilera
- Directed network modules
Gergely Palla, Ille’s J Farkas, Pe’ter Pollner, Imre Dere’nyi and Tama’s Vicsek
- Topology control with IPD network creation games
Jan C Scholz and Martin O W Greiner
- Robustness of cooperation in the evolutionary prisoner’s dilemma on complex networks
J Poncela, J Go’mez-Garden~es, L M Flori’a and Y Moreno
- The interplay of universities and industry through the FP5 network
Juan A Almendral, J G Oliveira, L Lo’pez, Miguel A F Sanjua’n and J F F Mendes
- Bounding network spectra for network design
Adilson E Motter
- Accelerating networks
David M D Smith, Jukka-Pekka Onnela and Neil F Johnson
- Weighted network modules
Ille’s Farkas, Da’niel A’bel, Gergely Palla and Tama’s Vicsek
- Analysis of a large-scale weighted network of one-to-one human communication
Jukka-Pekka Onnela, Jari Sarama”ki, Jo”rkki Hyvo”nen, Ga’bor Szabo’, M Argollo de Menezes, Kimmo Kaski, Albert-La’szlo’ Baraba’si and Ja’nos Kerte’sz
- Structurefunction relationship in complex brain networks expressed by hierarchical synchronization
Changsong Zhou, Lucia Zemanova’, Gorka Zamora-Lo’pez, Claus C Hilgetag and Ju”rgen Kurths
- Fractality and self-similarity in scale-free networks
J S Kim, K-I Goh, B Kahng and D Kim
- Size reduction of complex networks preserving modularity
A Arenas, J Duch, A Ferna’ndez and S Go’mez
- Fractal and transfractal recursive scale-free nets
Herna’n D Rozenfeld, Shlomo Havlin and Daniel ben-Avraham
- Building catastrophes: networks designed to fail by avalanche-like breakdown
M Woolf, Z Huang and R J Mondrago’n
- Structural constraints in complex networks
S Zhou and R J Mondrago’n
- The complex network of musical tastes
Javier M Buldu’, P Cano, M Koppenberger, Juan A Almendral and S Boccaletti
Complex Networks: Structure, Robustness and Function
R. Cohen and S. Havlin
Cambridge University Press, 2010
Chinese Edition, Cambridge University Press, 2015
Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks.
Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks.
Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field. End-of-chapter review questions help students monitor their own understanding of the materials presented.
Frontiers in Condensed Matter Physics
Proceedings of the 3rd Bar-Ilan Conference 1990
Editors: M. Deutsch, S. Havlin, M. Kaveh and Y. Yeshurun
Physica A 168, North Holland, 1990.
Models for Non-Classical Reaction Rates
Proceedings of the NIH Conference 1990.
Editors: S. Havlin, R. Nossal and M. Shlezinger
J. Stat. Physics ,63 ,1991.
Frontiers in Condensed Matter Physics
Proceedings of the 4th Bar-Ilan International Conference, 1993.
Editors: I. Kanter, M. Deutsch, S. Havlin, M. Kaveh and Y. Yeshurun
Physica A 200, North Holland, 1993.
Frontiers in Condensed Matter Physics
Proceedings of the 5th Bar-Ilan International Conference
on Physics of Complex Systems, 1997;
Editors: Y. Rabin, B. Ehrenberg, S. Havlin, K. Kessler, H. Taitelbaum
Physica A 249, North Holland, 1998.
Mesoscopics, Fractals and Neural Networks:
Proceedings of the Minerva Workshop, 1997
Editors: R. Berkovits, S. Havlin, I. Kanter and M. Kaveh
Philos. Mag. B 77, 1998
Percolation And Disordered Systems Theory And Applications:
Proceedings of the Giessen conference 1998
Editors: A. Bunde and S. Havlin
Physica A 266, 1999
Randomness and complexity
Proceedings of the international Worksop in honor of SHLOMO HAVLIN’s 60-th birthday.
Eilat, Israel, 5-9 January 2003