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.
Graphical abstract
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Bishop, Foreword, Eur. Phys. J. Special Topics 214, 1 (2012)
D. Helbing, Introduction, Eur. Phys. J. Special Topics 214, 5 (2012)
D. Helbing, S. Bishop, R. Conte, P. Lukowicz, J.B. McCarthy, Eur. Phys. J. Special Topics 214, 11 (2012)
A. Carbone, M. Ajmone-Marsan, K. Axhausen, M. Batty, M. Masera, E. Rome, D. Helbing, Eur. Phys. J. Special Topics 214, 435 (2012)
S. Bishop, D. Helbing, P. Lukowicz, R. Conte, Proc. Comp. Sci. 7, 34 (2011)
D. Helbing, S. Balietti, Eur. Phys. J. Special Topics 195, 3 (2011)
D. Helbing, S. Balietti, S. Bishop, P. Lukowicz, Eur. Phys. J. Special Topics 195, 165 (2011)
M.E.J. Newman, A.-L. Barabási, D.J. Watts, The structure and dynamics of networks (Princeton University Press, Princeton, NJ, 2006)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)
M.E.J. Newman, Networks: An introduction (Oxford University Press, Oxford, 2010)
R. Cohen, S. Havlin, Complex networks: structure, robustness and function (Cambridge Univ. Press, 2010)
F. Liljeros, C.R. Edling, L.A.N. Amaral, H.E. Stanley, Y. Aberg, Nature 411, 6840 (2001)
M. Faloutsos, P. Faloutsos, C. Faloutsos, SIGCOMM Comput. Commun. Rev. 29, 251 (1999)
A.-L. Barabási, R. Albert, Science 286, 509 (1999)
R. Pastor-Satorras, A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001)
R. Cohen, S. Havlin, D. Ben-Avraham, Phys. Rev. Lett. 91, 247901 (2003)
F. Radicchi, S. Fortunato, C. Castellano, Proc. Natl. Acad. Sci. USA 105, 17268 (2008)
G. Bonanno, G. Caldarelli, F. Lillo, S. Micciché, N. Vandewalle, R.N. Mantegna, Eur. Phys. J. B 38, 363 (2003)
S. Solomon, G. Weisbuch, L. de Arcangelis, N. Jan, D. Stauffer, Physica A 277, 239 (2000)
S. Solomon, E. Shir, S. Kirkpatrik, in Proceedings of AISB03 Adaptive Agents and Multi-Agent Systems, edited by D. Kazakov, E. Alonso, D. Kudenko (Aberystwyth, 2004)
J. Shao, S. Havlin, H.E. Stanley, Phys. Rev. Lett. 103, 018701 (2009)
M. Granovetter, Amer. J. Sociol. 78, 1360 (1973)
J.-P. Onnela, J. Saramäki, J. Hyvonen, G. Szabó, D. Lazer, K. Kaski, J. Kertész, A.-L. Barabási, Proc. Natl. Acad. Sci. USA 104, 7332 (2007)
S. Cantono, S. Solomon, New J. Phys. 12, 075038 (2010)
Introductory chapter of this issue, Eur. Phys. J. Special Topics 214 (2012)
R. Itzhak, L. Muchnik, T. Erez, S. Solomon, J. Goldenberg, Y. Louzoun, Physica A 389, 5308 (2010)
N. Fujiwara, J. Kurths, A. Díaz-Guilera, Phys. Rev. E 83, 025101 (2011)
C. Nardini, B. Kozma, A. Barrat, Phys. Rev. Lett. 100, 158701 (2008)
G. Iniguez, J. Kertész, K. Kaski, R.A. Barrio, Phys. Rev. E 80, 066119 (2009)
R. Parshani, M. Dickison, R. Cohen, H.E. Stanley, S. Havlin, EPL 90, 38004 (2010)
M. Karsai, M. Kivelä, R.K. Pan, K. Kaski, J. Kertész, A.-L. Barabási, J. Saramäki, Phys. Rev. E 83, 025102(R) (2011)
A.-L. Barabási, Nature 435, 207 (2005)
M. San Miguel, J.H. Johnson, J. Kertesz, K. Kaski, A. Diaz-Guilera, R. S. MacKay, V. Loreto, P. Erdi, D. Helbing, Eur. Phys. J. Special Topics 214, 245 (2012)
S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature 464, 08932 (2010)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
K. Kosmidis, S. Havlin, A. Bunde, EPL 82, 48005 (2008)
L. Daqing, K. Kosmidis, A. Bunde, S. Havlin, Nature Phys. 7, 481 (2011)
G. Krings, F. Calabrese, C. Ratti, V.D. Blondel, J. Stat. Mech. L07003 (2009)
P. Wang, M.C. González, C.A. Hidalgo, A.L. Barabási, Science 324, 1071 (2009)
S. Havlin, Science 324, 1023 (2009)
C.M. Schneider, T. Mihaljev, S. Havlin, H.J. Herrmann, [arXiv:1102.1929] (2011)
C.M. Schneider, A.A. Moreira, J.S. Andrade Jr., S. Havlin, H.J. Herrmann, Proc. Natl. Acad. Sci. USA 108, 3838 (2011)
A. Garas, P. Argyrakis, C. Rozenblat, M. Tomassini, S. Havlin, New J. Phys. 12, 113043 (2010)
D.Y. Kenett, M. Raddant, T. Lux, E. Ben-Jacob, PLoS ONE 7, e31144 (2012)
M. Kitsak, L.K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H.E. Stanley, H.A. Makse, Nature Phys. 6, 888 (2010)
S. Lämmer, D. Helbing, J. Stat. Mech.-Theory E. 2008, 04019 (2008)
G. Li, S.D.S. Reis, A.A. Moreira, S. Havlin, H.E. Stanley, J.S. Andrade Jr., Phys. Rev. Lett. 104, 018701 (2010)
A. Gozolchiani, K. Yamasaki, S. Havlin, [arXiv:1010.2605] (in print) (2011)
R. Albert, H. Jeong, A.L. Barabasi, Nature 406, 378 (2000)
R. Cohen, K. Erez, D. Ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000)
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
R. Pastor-Satorras, A. Vespignani, Evolution and structure of the Internet: A statistical physics approach (Cambridge University Press, Cambridge, 2006)
S.N. Dorogovtsev, J.F.F. Mendes, Evolution of networks: From biological nets to the Internet and WWW (Oxford University Press, New York, 2003)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
G. Caldarelli, Scale-free networks (Oxford University Press, Oxford, 2007)
G. Caldarelli, A. Vespignani, Large scale structure and dynamics of complex networks: From information technology to finance and natural science (World Scientific, Singapore, 2007)
A. Barrat, M. Barthélemy, A. Vespignani, Dynamical processes on complex networks (Cambridge Univ. Press, 2008)
D. Helbing, D. Armbruster, A. Mikhailov, E. Lefeber, Physica A 363, 1 (2006)
D. Helbing, J. Siegmeier, S. Lämmer, Networks Heterogeneous Media 2, 193 (2007)
T. Becker, M.E. Beber, K. Windt, M-T. Hütt, D. Helbing, J. Stat. Mech. P05004 (2011)
S. Carmi, Z. Wu, E. Lopez, S. Havlin, H.E. Stanley, Eur. Phys. J. B 57, 165 (2007)
E. Lopez, S. Carmi, S. Havlin, S.V. Buldyrev, H.E. Stanley, Physica D 224, 69 (2006)
R. Kinney, P. Crucitti, R. Albert, V. Latora, Eur. Phys. J. B 46, 101 (2005)
A. Kesting, M. Treiber, D. Helbing, IEEE Intell. Transportation Syst. 11, 172 (2010)
R. Sipahi, S. Lämmer, D. Helbing, J. Dynamic Systems, Meas. Control 131, 021005 (2009)
R. Cohen, K. Erez, D. Ben-Avraham, S. Havlin, Phys. Rev. Lett. 86, 3682 (2001)
D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000)
Y. Chen, G. Paul, S. Havlin, F. Liljeros, H.E. Stanley, Phys. Rev. Lett. 101, 058701 (2008)
A.E. Motter, Y.C. Lai, Phys. Rev. E 66, 065102 (2002)
D. Helbing, C. Kühnert, Physica A 328, 584 (2003)
A.E. Motter, Phys. Rev. Lett. 93, 098701 (2004)
L. Buzna, K. Peters, D. Helbing, Physica A 363, 132 (2006)
L. Buzna, K. Peters, H. Ammoser, C. Kühnert, D. Helbing, Phys. Rev. E 75, 056107 (2007)
K. Peters, L. Buzna, D. Helbing, Int. J. Crit. Infrastructures 4, 46 (2008)
I. Simonsen, L. Buzna, K. Peters, S. Bornholdt, D. Helbing, Phys. Rev. Lett. 100, 218701 (2008)
D. Balcan, V. Colizza, B. Goncalves, H. Hu, J.J. Ramasco, A. Vespignani, Proc. Natl. Acad. Sci. USA 106, 21484 (2009)
H. Hooyberghs, B. van Schaeybroeck, A.A. Moreira, J.S. Andrade Jr., H.J. Herrmann, J.O. Indekeu, Phys. Rev. E 81, 011102 (2010)
C.M. Schneider, R.F.S. Andrade, T. Shinbrot, H.J. Herrmann, EPL 95, 16001 (2011)
C.M. Schneider, L. de Arcangelis, H.J. Herrmann, EPL 95, 16005 (2011)
D. Helbing, H. Ammoser, C. Kühnert, Physica A 363, 141 (2006)
A. Moreira, J.S. Andrade Jr., H.J. Herrmann, J.O. Indekeu, Phys. Rev. Lett. 102, 018701 (2009)
A. Gulfraind, PLoS one 5, e13448 (2010)
J. Shao, S.V. Buldyrev, S. Havlin, H.E. Stanley, Phys. Rev. E 83, 036116 (2011)
H.J. Herrmann, C.M. Schneider, A.A. Moreira, J.S. Andrade Jr., S. Havlin, J. Stat. Mech. P01027 (2011)
A. Vespignani, Nature 464, 984 (2010)
V. Rosato, L. Issacharoff, F. Tiriticco, S.S. Meloni, S.D. Porcellinis, R. Setola, Int. J. Critical Infrastructures 4, 63 (2008)
F. Schweitzer, G. Fagiolo, D. Sornette, F. Vega-Redondo, A. Vespignani, D.R. White, Science 325, 422 (2009)
R. Parshani, S.V. Buldyrev, S. Havlin, Phys. Rev. Lett. 105, 048701 (2010)
P. Erdös, A. Rényi, Publ. Math. Debrecen 6, 290 (1959)
P. Erdös, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960)
J. Chalupa, P.L. Leath, G.R. Reich, J. Phys. C 12, L31 (1979)
B. Bollobás, Random graphs (Academic, 1985)
A. Bunde, S. Havlin, Fractals and disordered systems (Springer, Berlin, 1996)
C. Moukarzel, P.M. Duxbury, P.L. Leath, Phys. Rev. E 55, 5800 (1997)
M.L. Sachtjen, B.A. Carreras, V.E. Lynch, Phys. Rev. E 61, 4877 (2000)
D.J. Watts, Proc. Natl. Acad. Sci. USA 99, 5766 (2002)
Y. Moreno, R. Pastor-Satorras, A. Vazquez, A. Vespignani, EPL 62, 292 (2003)
R. Parshani, S.V. Buldyrev, S. Havlin, Proc. Natl. Acad. Sci. USA 108, 1007 (2011)
R. Parshani, C. Rozenblat, D. Ietri, C. Ducruet, S. Havlin, EPL 92, 68002 (2010)
X.Q. Huang, J.X. Gao, S.V. Buldyrev, S. Havlin, H.E. Stanley, Phys. Rev. E 83, 065101 (2011)
C.M. Schneider, N.A.M. Araújo, S. Havlin, H.J. Herrmann [arXiv:1106.3234] (2011)
P. Holme, J. Saramaki [arXiv:1108.1780] (2011)
M. Schönhoff, A. Kesting, M. Treiber, D. Helbing, Physica A 363, 73 (2006)
M. Barthélemy, Phys. Rep. 499, 1 (2011)
A.A. Tsonis, K.L. Swanson, P.J. Roebber, Bull. Am. Meteorol. Soc. 87, 585 (2006)
A.A. Tsonis, G. Wang, K.L. Swanson, F.A. Rodrigues, L.D. Costa, Clim. Dyn. 37, 933 (2011)
A. Gozolchiani, K. Yamasaki, O. Gazit, S. Havlin, EPL 83, 28005 (2008)
K. Yamasaki, A. Gozolchiani, S. Havlin, Phys. Rev. Lett. 100, 228501 (2008)
J.F. Donges, Y. Zou, N. Marwan, J. Kurths, EPL 87, 48007 (2009)
J.F. Donges, H.C.H, Schultz, N. Marwan, Y. Zou, J. Kurths, Eur. Phys. J. B 84, 635 (2011)
N. Malik, B. Bookhagen, N. Marwan, J. Kurths, Clim. Dyn. 39, 971 (2012)
M.E.J. Newman, Proc. Natl. Acad. Sci. USA 98, 404 (2001)
M. Girvan, M.E.J. Newman, Proc. Natl. Acad. Sci. USA 99, 7821 (2002)
G. Palla, I. Derenyi, I. Farkas, T. Vicsek, Nature 435, 814 (2005)
G. Kossinets, D. Watts, Science 311, 88 (2006)
Webpage http://empcommission.org/docs/A2473-EMP_Commission-7MB.pdf (retrieved 2011)
Y. Wu, C. Zhou, J. Xiao, J. Kurths, H.J. Schellnhuber, Proc. Natl. Acad. Sci. USA 107, 42 (2010)
D.Y. Kenett, M. Tumminello, A. Madi, G. Gur-Gershgoren, R.N. Mantegna, E. Ben-Jacob, PLoS one 5, e15032 (2010)
Y. Shapira, D.Y. Kenett, E. Ben-Jacob, Eur. Phys. J. B 72, 659 (2009)
D.Y. Kenett, Y. Shapira, A. Madi, S. Bransburg-Zabary, G. Gur-Gershgoren, E. Ben-Jacob, PLoS one 6, e19378 (2011)
D.Y. Kenett, Y. Shapira, G. Gur-Gershgoren, E. Ben-Jacob, J. Eng. Tech. Sci. Rev. 4, 218 (2012)
D.Y. Kenett, T. Preis, G. Gur-Gershgoren, E. Ben-Jacob, Int. J. Bifurcat. Chaos 22, 1250181 (2012)
D.Y. Kenett, Y. Shapira, G. Gur-Gershgoren, E. Ben-Jacob, J. Eng. Sci. Tech. Rev. 4, 218 (2012)
D.Y. Kenett, M. Raddant, L. Zatlavi, T. Lux, E. Ben-Jacob, Int. J. Mod. Phys. Conf. Ser. 16, 13 (2012)
B. Tóth, J. Kertész, Physica A 360, 505 (2006)
A. Madi, D.Y. Kenett, S. Bransburg-Zabary, Y. Merbl, F.J. Quintana, S. Boccaletti, A.I. Tauber, R. Cohen, E. Ben-Jacob, Chaos 21, 016109 (2011)
Y.N. Kenett, D.Y. Kenett, E. Ben-Jacob, M. Faust, PLoS one 6, e23912 (2011)
A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)
I. Sendina-Nadal, Y. Ofran, J.A. Almendral, J.M. Buldu, I. Leyva, D.Q. Li, S. Havlin, S. Boccaletti, PLoS one 6, e17679 (2011)
C. Qian, Y.B. Wang, J.D. Cao, J.Q. Lu, J. Kurths, EPL 93, 68006 (2011)
G. Zamora-López, C. Zhou, J. Kurths, Front. Neurosci. 5, 83 (2011)
L. Zemanova, G. Zamora, C. Hilgetag, J. Kurths, Phys. Rev. Lett. 97, 238103 (2006)
L. Kovanen, M. Karsai, K. Kaski, J. Kertész, J. Saramaki [arXiv 1107.5646] (2011)
M.G. Zimmermann, V.M. Eguluz, M. San Miguel, Phys. Rev. E 69, 065102 (2004)
T. Gross, B. Blasius, J. R. Soc. Interface 5, 259 (2008)
S. Fortunato, Physics Reports 486, 75 (2010)
P.J. Mucha, T. Richardson, K. Macon, M.A. Porter, J.P. Onnela, Science 328, 876 (2010)
C. Kühnert, D. Helbing, G.B. West, Physica A 363, 96 (2006)
Y. Louzoun, L. Muchnick, S. Solomon, Bioinformatics 22, 581 (2006)
F. Lillo, E. Moro, G. Vaglica, R.N. Mantegna, New J. Phys. 10, 043019 (2008)
G.-H. Mu, W.-X. Zhou, W. Chen, J. Kertész, New J. Phys. 12, 075037 (2010)
R. Wimberley, L. Morris, G. Fulkerson, The Rural Sociologist 27, 42 (2007)
D.Y. Kenett, J. Portugali, Proc. Natl. Acad. Sci. USA 109, 11472 (2012)
J. Portugali, Complexity, Cognition and the City (Springer 2011)
M. Batty, Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals (MIT Press 2007)
M. Batty, Science 319, 769 (2008)
M. Batty, Building Res. Information 38, 123 (2010)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Havlin, S., Kenett, D.Y., Ben-Jacob, E. et al. Challenges in network science: Applications to infrastructures, climate, social systems and economics. Eur. Phys. J. Spec. Top. 214, 273–293 (2012). https://doi.org/10.1140/epjst/e2012-01695-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2012-01695-x