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In this paper, we explore the problem of establishing a network among the stocks of a market at high frequency level and give an application to program trading. Our work uses high frequency data from the National Stock Exchange, India, for the year 2014. To begin, we analyse the spectrum of the correlation matrix to establish the presence of linear relations amongst the stock returns. A comparison of correlations with pairwise mutual information shows the further existence of non-linear relations which are not captured by correlation. We also see that the non-linear relations are more pronounced at the high frequency level in comparison to the daily returns used in earlier work. We provide two applications of this approach. First, we construct minimal spanning trees for the stock network based on mutual information and study their topology. The year 2014 saw the conduct of general elections in India and the data allows us to explore their impact on aspects of the network, such as the scale-free property and sectorial clusters. Second, having established the presence of non-linear relations, we would like to be able to exploit them. Previous authors have suggested that peripheral stocks in the network would make good proxies for the Markowitz portfolio but with a much smaller number of stocks. We show that peripheral stocks selected using mutual information perform significantly better than ones selected using correlation. [ABSTRACT FROM AUTHOR]

In this paper, we model the bus networks of six major Indian cities as graphs in L-space, and evaluate their various statistical properties. While airline and railway networks have been extensively studied, a comprehensive study on the structure and growth of bus networks is lacking. In India, where bus transport plays an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer basic questions on its evolution, growth, robustness and resiliency. Although the common feature of small-world property is observed, our analysis reveals a wide spectrum of network topologies arising due to significant variation in the degree-distribution patterns in the networks. We also observe that these networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, such as Internet, WWW and airline, that are virtual, bus networks are physically constrained. Our findings therefore, throw light on the evolution of such geographically and constrained networks that will help us in designing more efficient bus networks in the future. [ABSTRACT FROM AUTHOR]