The effects of node exclusion on the centrality measures in graph models of interacting economic agents

• We model possible damages in network to apply in financial market.
• The damage is quantified with Information Centrality to crash in Stock Market.
• We analyzed the effect of deleting some edges on the architecture.
• It is possible to simulate problems in terms of weakening the links between the economic agents.

This work concerns the study of the effects felt by a network as a whole when a specific node is perturbed. Many real world systems can be described by network models in which the interactions of the various agents can be represented as an edge of a graph. With a graph model in hand, it is possible to evaluate the effect of deleting some of its edges on the architecture and values of nodes of the network. Eventually a node may end up isolated from the rest of the network and an interesting problem is to have a quantitative measure of the impact of such an event. For instance, in the field of finance, the network models are very popular and the proposed methodology allows to carry out “what if” tests in terms of weakening the links between the economic agents, represented as nodes.The two main concepts employed in the proposed methodology are (i) the vibrational IC—Information Centrality, which can provide a measure of the relative importance of a particular node in a network and (ii) autocatalytic networks that can indicate the evolutionary trends of the network. Although these concepts were originally proposed in the context of other fields of knowledge, they were also found to be useful in analyzing financial networks.In order to illustrate the applicability of the proposed methodology, a case of study using the actual data comprising stock market indices of 12 countries is presented.