  Most of the real world complex networks such as the Internet, World Wide Web
and collaboration networks are huge; and to infer their structure and dynamics
one requires handling large connectivity (adjacency) matrices. Also, to find
out the spectra of these networks, one needs to perform the EigenValue
Decomposition(or Singular Value Decomposition for bipartite networks) of these
large adjacency matrices or their Laplacian matrices. In the present work, we
proposed randomized versions of the existing heuristics to infer the norm and
the spectrum of the adjacency matrices. In an earlier work [1], we used Subset
Selection (SS) procedure to obtain the critical network structure which is
smaller in size and retains the properties of original networks in terms of its
Principal Singular Vector and eigenvalue spectra. We now present a few
randomized versions of SS (RSS) and their time and space complexity calculation
on various benchmark and real-world networks. We find that the RSS based on
using QR decomposition instead of SVD in deterministic SS is the fastest. We
evaluate the correctness and the performance speed after running these
randomized SS heuristics on test networks and comparing the results with
deterministic counterpart reported earlier. We find the proposed methods can be
used effectively in large and sparse networks; they can be extended to analyse
important network structure in dynamically evolving networks owing to their
reduced time complexity.
