标题： 中心性悖论：为什么你的朋友总是更重要 显示英文标题

标题： The Centrality Paradox: Why Your Friends Are Always More Important

摘要： 我们重新审视经典的友谊悖论，该悖论指出，平均而言，一个人的朋友至少和自己有同样多的朋友，并将其推广到各种网络中心性度量。 特别是，我们证明对于任何不可约的无向图$G$，度数、特征向量中心性、路径计数、Katz 中心性和 PageRank 中心性的“朋友平均值”超过全局平均值。 我们证明该结果来自于对应于 Perron 特征值的特征向量的变分特性。 显示英文摘要

摘要： We revisit the classical friendship paradox which states that on an average one's friends have at least as many friends as oneself and generalize it to a variety of network centrality measures. In particular, we show that for any irreducible, undirected graph $G$, the "friends-average" of degree, eigenvector-centrality, walk-count, Katz, and PageRank centralities exceeds the global average. We show that the result follows from the variational characterisation of the eigenvector corresponding to the Perron eigenvalue.