Optimality problem of network topology in stocks market analysis

• The MST-based network topology is not optimal in terms of topological properties.
• Therefore, the economic interpretation of that network might be misleading.
• A set of optimality criteria and a selection method of an optimal MST are developed.
• The advantage of the proposed method is illustrated by using NYSE data.

Since its introduction fifteen years ago, minimal spanning tree has become an indispensible tool in econophysics. It is to filter the important economic information contained in a complex system of financial markets’ commodities. Here we show that, in general, that tool is not optimal in terms of topological properties. Consequently, the economic interpretation of the filtered information might be misleading. To overcome that non-optimality problem, a set of criteria and a selection procedure of an optimal minimal spanning tree will be developed. By using New York Stock Exchange data, the advantages of the proposed method will be illustrated in terms of the power-law of degree distribution.