ABSTRACT

In digraphs representing asymmetric relations, the measured scores of previous spectral rankings are usually dominated by nodes in the largest strongly connected component. In our previous work, we proposed hierarchical alpha centrality to give higher scores for more reachable nodes not in the largest strongly connected component. However, without careful consideration of damping parameters, the scores obtained by this method may be unbounded. In this paper, we normalize the adjacency matrix to be stochastic, subsequently damping the resulting Markov chain with a reciprocal perturbation at each and every non-zero transition, and propose a new hierarchical measure of centrality for asymmetric relations. The proposed measure simplifies damping and ensures that the measured scores are bounded.

摘要

在表示不对称关系的有向图中，先前光谱排名的测量分数通常由最大强连通分量中的节点控制。在我们之前的工作中，我们提出了分层 alpha 中心性，以便为不在最大强连接组件中的更可达节点提供更高的分数。但是，如果不仔细考虑阻尼参数，这种方法获得的分数可能是无界的。在本文中，我们将邻接矩阵归一化为随机的，随后在每个非零转换处用相互扰动来阻尼生成的马尔可夫链，并提出一种新的不对称关系中心性的分层度量。所提出的措施简化了阻尼并确保测量的分数是有界的。