复杂网络的迭代全局模型
Iterated Global Models for Complex Networks
摘要：
我们引入迭代全局模型作为一个确定性的图形过程，模拟复杂网络的几个属性。在这个模型中，对于每个指定基数的节点集合$S$，我们添加一个新节点，该节点与$S$中的每个节点相邻。我们关注的情况下，$S$的大小大约是一半的节点数在每个时间步，我们称之为半模型。半模型可证明生成的图随着时间的推移而变密，具有差的谱扩展和低直径。我们推导出团，色，和控制数的模型所产生的图。
英文摘要：
We introduce the Iterated Global model as a deterministic graph process that simulates several properties of complex networks. In this model, for every set $S$ of nodes of a prescribed cardinality, we add a new node that is adjacent to every node in $S$. We focus on the case where the size of $S$ is approximately half the number of nodes at each time-step, and we refer to this as the half-model. The half-model provably generate graphs that densify over time, have bad spectral expansion, and low diameter. We derive the clique, chromatic, and domination numbers of graphs generated by the model.
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