Author(s): Kaiser M
Abstract: Almost all real-world networks are distributed in space. In many of these networks, more short- than long-distance connections exist. Thus, there is a preference to minimize the length of connections. Such networks often exhibit properties of small-world, scale-free or multi-clustered networks. However, previous models for development, where only distance between nodes is considered when establishing a connection, were unable to yield spatial graphs with these properties. I present a new model for spatial graph development that can generate small-world networks. Notably, also scale-free networks (similar to the German highway system or the yeast protein-protein interaction network) can be generated without using preferential attachment. The final topology of the network depended on whether the growing network reached spatial limits during development or not. Furthermore, different models for network evolution (limited, unlimited and preferential attachment) could be distinguished by observing the change of density and clustering coefficient over time. Spatial growth was able to yield networks similar to real-world spatial networks. As a case study, I generated networks similar to cortical networks. I found that not only global network properties but also wiring properties were similar. In addition, multiple clusters could be generated by introducing time windows.
Keywords: spatial graphs, biological networks, scale-free, small-world