Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valuable information about connectivity, as well as about the relative importance or centrality of nodes. Another popular approach to rank the nodes of a network is to compute the left Perron vector of the adjacency matrix for the network. The present article addresses the problem of evaluating matrix functions, as well as computing an approximation to the left Perron vector, when only some of the columns and/or some of the rows of the adjacency matrix are known. Applications to network analysis are considered, when only some sampled columns and/or rows of the adjacency matrix that defines the network are available. A sampling scheme that takes the connectivity of the network into account is described. Computed examples illustrate the performance of the methods discussed.

中文翻译：

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部分已知矩阵的函数和特征向量在网络分析中的应用

矩阵函数在应用数学中扮演着重要的角色。特别是在网络分析中，与网络相关联的邻接矩阵的指数提供了有关连通性以及节点的相对重要性或中心性的宝贵信息。另一种对网络节点进行排序的流行方法是计算网络邻接矩阵的左 Perron 向量。本文解决了评估矩阵函数的问题，以及计算左 Perron 向量的近似值时，当仅知道邻接矩阵的某些列和/或某些行时。当定义网络的邻接矩阵中只有一些采样列和/或行可用时，考虑网络分析的应用。描述了考虑网络连通性的采样方案。计算示例说明了所讨论方法的性能。