论文标题
具有异质密度网络的潜在泊松模型
Latent Poisson models for networks with heterogeneous density
论文作者
论文摘要
与网络的总大小相比，经验网络通常在全球稀疏，每个节点的平均连接数量少。但是，这种稀疏性往往不是均匀的，并且网络也可以是局部密集的，例如，几个节点连接到网络其余部分的大部分，或与它们之间具有很大连接可能性的一小部分节点。在这里，我们展示了产生隐藏多编码的潜在泊松模型如何有效地捕获这种密度异质性，而在数学上比直接模拟简单图形的某些替代方案更具易处理性。我们展示了如何从简单图上的数据中重建这些潜在的多编码，以及这如何使我们能够将分离的程度度相关性与施加程度序列的约束分开，并改善与经验相关的情景中社区结构的识别。
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense, for example with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models which generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle disassortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community structure in empirically relevant scenarios.
