Matrix computations (3rd ed.)
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Google's PageRank and Beyond: The Science of Search Engine Rankings
Google's PageRank and Beyond: The Science of Search Engine Rankings
A lock-and-key model for protein--protein interactions
Bioinformatics
Spectral clustering and its use in bioinformatics
Journal of Computational and Applied Mathematics
Movies and Actors: Mapping the Internet Movie Database
IV '07 Proceedings of the 11th International Conference Information Visualization
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
CONTEST: A Controllable Test Matrix Toolbox for MATLAB
ACM Transactions on Mathematical Software (TOMS)
Discrete Applied Mathematics
Invariants of distance k-graphs for graph embedding
Pattern Recognition Letters
Proceedings of the 21st ACM international conference on Information and knowledge management
Expanders, tropical semi-rings, and nuclear norms: oh my!
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
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The emerging field of network science deals with the tasks of modeling, comparing, and summarizing large data sets that describe complex interactions. Because pairwise affinity data can be stored in a two-dimensional array, graph theory and applied linear algebra provide extremely useful tools. Here, we focus on the general concepts of centrality, communicability, and betweenness, each of which quantifies important features in a network. Some recent work in the mathematical physics literature has shown that the exponential of a network's adjacency matrix can be used as the basis for defining and computing specific versions of these measures. We introduce here a general class of measures based on matrix functions, and show that a particular case involving a matrix resolvent arises naturally from graph-theoretic arguments. We also point out connections between these measures and the quantities typically computed when spectral methods are used for data mining tasks such as clustering and ordering. We finish with computational examples showing the new matrix resolvent version applied to real networks.