Spatial Effects on Complex Networks

复杂网络无处不在，在有机和无机物质中，在纳米和宏观尺度上，在自然和人为结构中。例子包括链接的分子或细胞结构，气候网络，通信网络（通过互联网，万维网和电话），但也社会社区，如各种俱乐部以及朋友网络和恐怖主义网络。了解这些网络的成长、结构和运作，对于使它们能够抵御失败、保护它们不受外部攻击，或者对于恐怖主义网络，能够以最有效的方式打击它们，都是至关重要的，其中许多网络，如因特网、社交网络或运输网络，都是建立在二维空间中的。在这项研究建议中，我们计划，第一次，以确定这种空间约束的拓扑结构，脆弱性和功能（运输，信息传播，流行病传播）的网络的影响，通过采用计算机模拟，渗透理论和适当的缩放理论。 我们计划不仅研究自然网络，而且还将开发能够考虑空间限制的模型。通过这样做，我们还希望最终达成更好和更有效的免疫战略，使网络不那么容易受到故障和外部干扰的影响，并将有助于获得更好和更有针对性的战略，以防止危险流行病的传播。

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.