Network analysis using Krylov subspace trajectories
CoRR(2024)
摘要
We describe a set of network analysis methods based on the rows of the Krylov
subspace matrix computed from a network adjacency matrix via power iteration
using a non-random initial vector. We refer to these node-specific row vectors
as Krylov subspace trajectories. While power iteration using a random initial
starting vector is commonly applied to the network adjacency matrix to compute
eigenvector centrality values, this application only uses the final vector
generated after numerical convergence. Importantly, use of a random initial
vector means that the intermediate results of power iteration are also random
and lack a clear interpretation. To the best of our knowledge, use of
intermediate power iteration results for network analysis has been limited to
techniques that leverage just a single pre-convergence solution, e.g., Power
Iteration Clustering. In this paper, we explore methods that apply power
iteration with a non-random inital vector to the network adjacency matrix to
generate Krylov subspace trajectories for each node. These non-random
trajectories provide important information regarding network structure, node
importance, and response to perturbations. We have created this short preprint
in part to generate feedback from others in the network analysis community who
might be aware of similar existing work.
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