Abstract
Social networks constitute the backbone underlying much of the interaction conducted in socioeconomic environments.1 Therefore, when this interaction attains a global reach it must have, as its counterpart, the emergence of a social network with a wide range of overall (typically indirect) connectivity. Naturally, for such a social network to emerge, agents must be able to link profitably. But this in turn demands that they display similar – at least compatible – behaviour. Thus, for example, they must use coherent communication procedures, share key social conventions, or have similar technical abilities. Here, we may quote the influential work of Castells (1996).
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Notes
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By way of illustration, one of the features of the process that introduces internode correlations can be explained as follows. First note that the postulated action dynamics leads high-degree nodes to exhibit, on average, stronger social “conformity” than lower-degree nodes. That is, they have a higher probability of choosing the action that is in the majority in the population. This in turn implies that links between high degree nodes will be formed with higher probability (that is, at a higher rate) than between lower-degree nodes. In the end, therefore, positive degree correlations will tend to arise, high-degree nodes being more likely to be connected to other high-degree nodes than what is prescribed by the unconditional average.
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As is well known in the theory of random networks, if a giant component exists in this context, it is unique.
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Of course, this presumes that the link between i and j is not already in place, which is an event that can be essentially ignored in large populations.
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Mathematically, the behavior displayed by the model reflects the onset of a bifurcation towards instability and equilibrium multiplicity as the parameter λ enters the region \({[\lambda _1 ,\lambda _2 ]}\). Such a bifurcation is analogous to that found by Brock and Hommes (1997) as the intensity of choice (here captured by either a change in the volatility rate λ or the choice-sensitivity parameter β) varies in a suitable range. See also Hommes (2006) for an extensive discussion of the issue.
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Acknowledgments
We thank an anonymous referee for very useful comments. Vega-Redondo also acknowledges financial support from the Spanish Ministry of Education under grant SEJ2007–62656.
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Ehrhardt, G., Marsili, M., Vega-Redondo, F. (2009). Homophily, Conformity, and Noise in the (Co-)Evolution of Complex Social Networks. In: Reggiani, A., Nijkamp, P. (eds) Complexity and Spatial Networks. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01554-0_8
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