Eur. Phys. J. Special Topics 214, 273-293 (2012)
https://doi.org/10.1140/epjst/e2012-01695-x

Regular Article

Challenges in network science: Applications to infrastructures, climate, social systems and economics

¹ Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
² School of Physics and Astronomy, Tel-Aviv University, Tel Aviv 69978, Israel
³ Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany
⁴ Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
⁵ Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, 8093 Zurich, Switzerland
⁶ Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany
⁷ Institute of Physics, Budapest University of Technology and Economics, 1111 Budapest, Hungary
⁸ School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
⁹ Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany
¹⁰ Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
¹¹ Department of Geography, Tel-Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
¹² Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

^a e-mail: havlins@gmail.com
^b e-mail: drorkenett@gmail.com
^c e-mail: eshelbj@gmail.com
^d e-mail: armin.bunde@physik.uni-giessen.de
^e e-mail: reuven@macs.biu.ac.il
^f e-mail: hans@ifb.baug.ethz.ch
^g e-mail: jan.kantelhardt@physik.uni-halle.de
^h e-mail: kertesz@phy.bme.hu
ⁱ e-mail: kirk@cs.huji.ac.il
^j e-mail: kurths@pik-potsdam.de
^k e-mail: juval@post.tau.ac.il
^l e-mail: sorin@vms.huji.ac.il

Received: 1 August 2012
Revised: 9 October 2012
Published online: 5 December 2012

Abstract

Network theory has become one of the most visible theoretical frameworks that can be applied to the description, analysis, understanding, design and repair of multi-level complex systems. Complex networks occur everywhere, in man-made and human social systems, in organic and inorganic matter, from nano to macro scales, and in natural and anthropogenic structures. New applications are developed at an ever-increasing rate and the promise for future growth is high, since increasingly we interact with one another within these vital and complex environments. Despite all the great successes of this field, crucial aspects of multi-level complex systems have been largely ignored. Important challenges of network science are to take into account many of these missing realistic features such as strong coupling between networks (networks are not isolated), the dynamics of networks (networks are not static), interrelationships between structure, dynamics and function of networks, interdependencies in given networks (and other classes of links, including different signs of interactions), and spatial properties (including geographical aspects) of networks. This aim of this paper is to introduce and discuss the challenges that future network science needs to address, and how different disciplines will be accordingly affected.