Dependency Network and Node Influence: Application to the Study of Financial Markets

Much effort has been devoted to assess the importance of nodes in complex networks. Examples of commonly used measures of node importance include node degree, node centrality and node vulnerability score (the effect of the node deletion on the network efficiency). Here we present a new approach to compute and investigate the mutual dependencies between network nodes from the matrices of node–node correlations. The dependency network approach provides a new system level analysis of the activity and topology of directed networks. The approach extracts topological relations between the networks nodes (when the network structure is analyzed), and provides an important step towards inference of causal activity relations between the network nodes (when analyzing the network activity). The resulting dependency networks are a new class of correlation-based networks, and are capable of uncovering hidden information on the structure of the network. Here, we present a review of the new approach, and an example of its application to financial markets. We apply the methodology to the daily closing prices of all Dow Jones Industrial Average (DJIA) index components for the period 1939–2010. Investigating