  In this brief review, we critically examine the recent work done on
correlation-based networks in financial systems. The structure of empirical
correlation matrices constructed from the financial market data changes as the
individual stock prices fluctuate with time, showing interesting evolutionary
patterns, especially during critical events such as market crashes, bubbles,
etc. We show that the study of correlation-based networks and their evolution
with time is useful for extracting important information of the underlying
market dynamics. We, also, present our perspective on the use of recently
developed entropy measures such as structural entropy and eigen-entropy for
continuous monitoring of correlation-based networks.
