  Most of the real world networks such as the internet network, collaboration
networks, brain networks, citation networks, powerline and airline networks are
very large and to study their structure, and dynamics one often requires
working with large connectivity (adjacency) matrices. However, it is almost
always true that a few or sometimes most of the nodes and their connections are
not very crucial for network functioning or that the network is robust to a
failure of certain nodes and their connections to the rest of the network. In
the present work, we aim to extract the size reduced representation of complex
networks such that new representation has the most relevant network nodes and
connections and retains its spectral properties. To achieve this, we use the
Subset Selection (SS) procedure. The SS method, in general, is used to retrieve
maximum information from a matrix in terms of its most informative columns. The
retrieved matrix, typically known as subset has columns of an original matrix
that have the least linear dependency. We present the application of SS
procedure to many adjacency matrices of real-world networks and model network
types to extract their subset. The subset owing to its small size can play a
crucial role in analyzing spectral properties of large complex networks where
space and time complexity of analyzing full adjacency matrices are too
expensive. The adjacency matrix constructed from the obtained subset has a
smaller size and represents the most important network structure. We observed
that the subset network which is almost half the size of the original network
has better information flow efficiency than the original network.
