This paper proposes a stochastic block model with dynamics where the population grows using preferential attachment. Nodes with higher weighted degree are more likely to recruit new nodes, and nodes always recruit nodes from their own community. This model can capture how communities grow or shrink based on their collaborations with other nodes in the network, where an edge represents collaboration on a project. Focusing on the case of two communities, we derive a deterministic approximation to the dynamics and characterize the phase transitions for diversity, i.e. the parameter regimes in which either one of the communities dies out or the two communities reach parity over time. In particular, we find that the minority may vanish when the probability of cross-community edges is low, even when cross-community projects are more valuable than projects with collaborators from the same community.

翻译：本文提出一种带有动力学的随机块模型，其中群体通过优先连接机制增长。具有更高加权度的节点更可能招募新节点，且节点始终从自身所属社区招募新节点。该模型能够捕捉社区如何根据其与网络中其他节点的协作（边代表项目协作）而扩大或缩小。针对双社区情形，我们推导出动力学的确定性近似，并刻画了多样性的相变特征，即描述其中某个社区消亡或两个社区随时间达到对等状态的参数区间。特别值得注意的是，我们发现当跨社区边概率较低时，即使跨社区项目比同社区合作项目更具价值，少数派社区仍可能消失。