Spatial Effects on Complex Networks

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Complex networks occur everywhere, in organic and inorganic matter, on nano and macro scales, in natural and anthropogenic structures. Examples include linked molecular or cellular structures, climate networks, communication networks (via Internet, WWW and telephones), but also social communities like clubs of all kinds as well as friend networks and terroristic networks. An understanding of the growth, structure and functioning of these networks is essential in order to make them resistant against failures, to protect them against external attacks or, as in the case of terroristic networks, to be able to fight them in the most efficient way.Many of these networks, like the Internet, social networks or transport networks, are settled in two-dimensional space. In this research proposal we plan, for the first time, to determine the effect of this spatial constraint on topology, vulnerability and functioning (transport, spreading of information, spreading of epidemics) of the networks, by employing computer simulations, percolation theory and appropriate scaling theories. We plan not only to study the natural networks, but will also develop models that are able to take into account the spatial constraints. By doing this, we also hope to arrive eventually at improved and more efficient immunization strategies that allow to make the networks less vulnerable against failures and external perturbations, and will also help to obtain an improved and more targeted strategy in fighting the spreading of hazardous epidemics.