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The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable… (More)

We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we describe fast and effective criteria for the selection of edges to be added to (or deleted from) a given directed network so as to enhance these network communicability measures.… (More)

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiveness and efficiency of our techniques in computing… (More)

In this document we summarize a few supplementary results to the accompanying paper. We give a detailed proof of the bounds on the normalized total communicability obtained via quadrature rules (Theorem 3.1, section 3). We also derive the computational costs for the heuristics introduced. Moreover, this document contains the results of some numerical… (More)

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiveness and efficiency of our techniques in computing… (More)

We propose a communication-driven mechanism for predicting triadic closure in complex networks. It is mathematically formulated on the basis of communicability distance functions that account for the " goodness " of communication between nodes in the network. We study 25 real-world networks and show that the proposed method predicts correctly 20% of triadic… (More)

The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable… (More)

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