论文标题
与社区结构的优先依恋图中的竞争类型
Competing types in preferential attachment graphs with community structure
论文作者
论文摘要
我们扩展了Antunović，Mossel和Rácz的两种优先依恋模型，在该模型中，每个新顶点根据其邻居的类型按照定义的规则进行类型，以结合社区结构，并研究社区之间每种类型同步的顶点的比例。行为既取决于社区结构的选择，也取决于类型分配规则。 本质上，单个社区模型具有多个可能的限制的所有情况，社区可能无法同步较弱的互动社区。即使单个社区模型几乎可以肯定地收敛到确定性极限，也无法保证同步。但是，我们为分配规则提供了自然条件，对于两个社区，结构都将暗示同步到该限制，并且每个限制都是最好的。 我们还举了一个例子，其中类型的比例几乎肯定不会融合，这在单个社区模型中是不可能的。
We extend the two-type preferential attachment model of Antunović, Mossel and Rácz, where each new vertex takes its type according to a defined rule based on the types of its neighbours, to incorporate community structure, and investigate whether the proportions of vertices of each type synchronise between communities. The behaviour depends both on the choice of community structure and on the type assignment rule. For essentially all cases where the single community model has more than one possible limit, communities may fail to synchronise for weakly interacting communities. Even when the single community model almost surely converges to a deterministic limit, synchronisation is not guaranteed. However, we give natural conditions on the assignment rule and, for two communities, on the structure, either of which will imply synchronisation to this limit, and each of which is essentially best possible. We also give an example where the proportions of types almost surely do not converge, which is impossible in the single community model.
