Notion of Graph Entanglement and Its Application for Stock Market Analysis

Abstract

The graph is one of the most convenient and widespread models of many real and formal systems. Indeed, this relatively simple notion turns out to be very useful in study, analysis and presentation of numerous systems, modeled by graphs. Various properties of modeled systems, sometimes indistinct and uncertain, are expressed as formal properties of modeling graphs. The property of graphs, introduced in the presented article, is just of this kind. It has different meaningful interpretations in different situations, but generally it describes complexity, entanglement, perplexity, intricacy and other hardly defined, though important, properties of various systems. The introduced notion, named as graph entanglement, turns out to be useful, in particular, for analysis of stock market behavior. This special application seems important and perspective; its first detailed presentation is the main goal of the article. The applications of the notion of graph entanglement in other domains are demonstrated in publication [1 — 4] and are not considered here.