Abstract
Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents’ strategies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–98
Axelrod R (1984) The Evolution of Cooperation. Basic Books, New York.
Bala V, Goyal S (2000) A noncooperative model of network formation. Econometrica 68:1181–1229
Barrat A, Weigt M (2000) On the properties of small-world network models. Eur Phys J B 13:547–560
Dorogovtsev SN, Mendes JFF (2003) Evolution of Networks: From Biological Nets to the Internet and WWW . Oxford University Press, Oxford
Ehrhardt G, Marsili M, Vega-Redondo F (2006) Diffusion and growth in an evolving network. Int J Game Theory 34:383–397
Erdős P, Rényi A (1959) On random graphs I. Publ Math Debrecen 6:290–297
Gila S, Zanette DH (2006) Coevolution of agents and networks: Opinion spreading and community disconnection. Phys¡??¿ Lett¡??¿ A 356:89–94
Gross T, Blasius B (2008) Adaptive coevolutionary networks: a review. J Roy Soc Interface 5:259–271
Holland PW, Leinhardt S (1972) Some evidence on the transitivity of positive interpersonal sentiment. Am J Sociol 72:1205–1209
Holme P, Ghoshal G (2006) Dynamics of networking agents competing for high centrality and low degree. Phys Rev Lett 96:098701
Holme P, Newman MEJ (2006) Nonequilibrium phase transition in the coevolution of networks and opinions. Phys Rev E 74:056108
Holme P, Zhao J (2007) Exploring the assortativity-clustering space of a network’s degree sequence. Phys Rev E 75:046111
Jackson MO, Wolinsky A (1996) A strategic model of social and economic networks. J Eco Theory 71:44–74
Kahneman D (2003) Maps of bounded rationality: psychology for behavioral economics. The Am Eco Rev 93:1449–1475
Knoke D (1990) Political Networks: The Structural Perspective. Cambridge University Press, Cambridge
Lindgren K, Nordahl MG (1994) Evolutionarycs of spatial games. Physica D 75:292–309
Nakao K (1990) Distribution of measures of centrality: Enumerated distributions of freeman’s graph centrality measures. Connections 13:10–22
Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256
Nowak M, Sigmund K (1992) A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner’s dilemma game. Nature 364:56–58
Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359:826–829
Rosvall M, Sneppen K (2003) Modelling dynamics of information networks. Phys Rev Lett 91:178701
Rosvall M, Sneppen K (2006) Modeling self-organization of communication and topology in social networks. Phys Rev E 74:016108
Sabidussi G (1966) The centrality index of a graph. Psychometrika 31:581–603
van Valen LM (1973) A new evolutionary law. Evol Theory 1:1–30
Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442
Weber M (1947) The Theory of Social and Economic Organization. Oxford University Press, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Holme, P., Ghoshal, G. (2009). The Diplomat’s Dilemma: Maximal Power for Minimal Effort in Social Networks. In: Gross, T., Sayama, H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01284-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-01284-6_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01283-9
Online ISBN: 978-3-642-01284-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)