  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.
