Stability Analysis of Company Co-Mention Network and Market Graph Over Time Using Graph Similarity Measures

Alexey Faizliev,Vladimir Balash,Vladimir Petrov,Dmitriy Melnichuk,Sergei Sidorov,Alexey Grigoriev

doi:10.3390/joitmc5030055

Alexey Faizliev, Vladimir Balash + Show 4 more

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https://doi.org/10.3390/joitmc5030055

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Abstract

The aim of the paper is to provide an analysis of news and financial data using their network representation. The formation of network structures from data sources is carried out using two different approaches: by building the so-called market graph in which nodes represent financial assets (e.g., stocks) and the edges between nodes stand for the correlation between the corresponding assets, by constructing a company co-mention network in which any two companies are connected by an edge if a news item mentioning both companies has been published in a certain period of time. Topological changes of the networks over the period 2005–2010 are investigated using the sliding window of six-month duration. We study the stability of the market graph and the company co-mention network over time and establish which of the two networks was more stable during the period. In addition, we examine the impact of the crisis of 2008 on the stability of the market graph as well as the company co-mention network. The networks that are considered in this paper and that are the objects of our study (the market graph and the company co-mention network) have a non-changing set of nodes (companies), and can change over time by adding/removing links between these nodes. Different graph similarity measures are used to evaluate these changes. If a network is stable over time, a measure of similarity between two graphs constructed for two different time windows should be close to zero. If there was a sharp change between the graphs constructed for two adjacent periods, then this should lead to a sharp increase in the value of the similarity measure between these two graphs. This paper uses the graph similarity measures which were proposed relatively recently. In addition, to estimate how the networks evolve over time we exploit QAP (Quadratic Assignment Procedure). While there is a sufficient amount of works studying the dynamics of graphs (including the use of graph similarity metrics), in this paper the company co-mention network dynamics is examined both individually and in comparison with the dynamics of market graphs for the first time.

Highlights

The modern economy is a complex system consisting of an enormous number of companies that interact with each other to achieve their own goals
The networks that are considered in this paper and that are the objects of our study have a non-changing set of nodes, and can change over time by adding/removing links between these nodes:
The results are similar to the results shown in Figure 6a. 39% of the variance is explained by the first principal component for the market graph and 13% for the co-mention graph

Summary

Introduction

The modern economy is a complex system consisting of an enormous number of companies that interact with each other to achieve their own goals. Modeling the aggregate as well as local behavior of such systems is an extremely important, albeit complex problem. One of the modern approaches to building models of economic or financial systems is graph models that are based on transforming empirical data into a network representation using additional reasonable assumptions. In such graphs, nodes usually correspond to companies, and edges between nodes reflect the relations between them. The following may serve an example of such relationships: J.

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