Community detection in large social networks is affected by degree
heterogeneity of nodes. The D-SCORE algorithm for directed networks was
introduced to reduce this effect by taking the element-wise ratios of the
singular vectors of the adjacency matrix before clustering. Meaningful results
were obtained for the statistician citation network, but rigorous analysis on
its performance was missing. First, this paper establishes theoretical
guarantee for this algorithm and its variants for the directed degree-corrected
block model (Directed-DCBM). Second, this paper provides significant
improvements for the original D-SCORE algorithms by attaching the nodes outside
of the community cores using the information of the original network instead of
the singular vectors.

该论文介绍了 D-SCORE 算法，用于大型社交网络中的社区检测，通过对邻接矩阵的奇异向量进行元素级别的比率来降低节点度量异质性的影响，理论上证明了这种算法及其变体在有向去噪格子模型下的性能对其进行了显着的改进，同时提供了在社区核外部分添加节点的新方法。

有向网络社区检测的光谱算法

Spectral Algorithms for Community Detection in Directed Networks

Community detection is a fundamental problem in network analysis, with
applications in many diverse areas. The stochastic block model is a common tool
for model-based community detection, and asymptotic tools for checking
consistency of community detection under the block model have been recently
developed. However, the block model is limited by its assumption that all nodes
within a community are stochastically equivalent, and provides a poor fit to
networks with hubs or highly varying node degrees within communities, which are
common in practice. The degree-corrected stochastic block model was proposed to
address this shortcoming and allows variation in node degrees within a
community while preserving the overall block community structure. In this paper
we establish general theory for checking consistency of community detection
under the degree-corrected stochastic block model and compare several community
detection criteria under both the standard and the degree-corrected models. We
show which criteria are consistent under which models and constraints, as well
as compare their relative performance in practice. We find that methods based
on the degree-corrected block model, which includes the standard block model as
a special case, are consistent under a wider class of models and that
modularity-type methods require parameter constraints for consistency, whereas
likelihood-based methods do not. On the other hand, in practice, the degree
correction involves estimating many more parameters, and empirically we find it
is only worth doing if the node degrees within communities are indeed highly
variable. We illustrate the methods on simulated networks and on a network of
political blogs.

本研究比较了标准随机块模型和修正度随机块模型下的几种社区检测准则，发现基于修正度随机块模型的方法在更广泛的模型和约束条件下具有一致性，但实际上它涉及到估计更多的参数，只有当社区内的节点度数确实高度变化时才值得使用。