Silvana Stefani

Some new results on the eigenvector centrality

In this article we establish new results on the components of the principal eigenvector in an undirected graph. Those results are particularly significant in relation to the concept of centrality in social networks. In particular degree centrality and eigenvector centrality are compared. We find further conditions, based on the spectral radius, on which nodes with highest degree centrality are also the most eigencentral.

Shareholding Networks and Centrality: An Application to the Italian Financial Market

In this paper we studied the Shareholding Network (SN) embedded in the Italian Stock Market (MIB). We identified the central companies both in the role of transferring information flows and controlling companies. To this end we used betweenness and flow betweenness centrality measures, together with in and out degree. We tested the scale-free property on in and out degree, betweenness and flow betweenness centrality. The effect of external shocks to SN and the different extent on which companies react to them is measured relating asset volatility and betweenness.

Speculative trading in mean reverting markets

Mean reversion is a feature largely recognized for the price processes of many financial securities and especially commodities. In the literature there are examples where some simple speculative strategies, before transaction costs, were devised to earn excess returns from such price processes. Actually, the gain opportunities of mean reversion must be corrected to account for transaction costs, which may represent a major issue. In this work we try to determine sufficient conditions for the parameters of a mean reverting price process as a function of transaction costs, to allow a speculative trader to have positive expectations when deciding to take a position. We estimate the mean reverting parameters for some commodities and correct them for transaction costs to assess whether the potential inefficiency is actually relevant for speculative purposes.

Extremal Properties of Graphs and Eigencentrality in Trees with a Given Degree Sequence

In this article, we investigate several issues related to the use of the index , known as the Zagreb index (see Gutman and Das, 2004) or “S-metric” (Alderson and Li, 2007). We present some new upper and lower bounds for S(G), in terms of the degree sequence of G. Then, we concentrate on trees and prove that in trees with maximum S(G) the eigenvector ordering is coherent with the degree ordering; that is, degree central vertices are also eigenvector central. This confirms results given in Bonacich (2007). Further, we show that these trees have minimum diameter and maximum spectral radius in the set of trees with a given degree sequence. A simple application to a company organizational network is provided.

The Academic Journal Ranking Problem: A Fuzzy-Clustering Approach

The Academic Journal Ranking Problem consists in formulating a formal assessment of scientific journals. An outcome variable must be constructed that allows valid journal comparison, either as a set of tiers (ordered classes) or as a numerical index. But part of the problem is also to devise a procedure to get this outcome, that is, how to get and use relevant data coming from expert opinions or from citations database. We propose a novel approach to the problem that applies fuzzy cluster analysis to peer reviews and opinion surveys. The procedure is composed of two steps: the first is to collect the most relevant qualitative assessments from international organizations (for example, the ones available in the Harzing database) and, as inductive analysis, to apply fuzzy clustering to determine homogeneous journal classes; the second deductive step is to determine the hidden logical rules that underlies the classification, using a classification tree to reproduce the same patterns of the first step.Our approach is applied to the classification of 138 academic journals that were selected by members of AMASES, an Italian mathematics association, as the most prominent journals of our field. The clusters that are determined by our method show that rankings are affected by two hidden dimensions: one is the academic prestige of a publication, but the other is the disciplinary diffusion of a mathematics subfield. In particular, mathematics journals that are close to finance or economics are usually ranked better than journals dealing with linear algebra or systems dynamics.

Higher order assortativity in complex networks

Assortativity was first introduced by Newman and has been extensively studied and applied to many real world networked systems since then. Assortativity is a graph metric and describes the tendency of high degree nodes to be directly connected to high degree nodes and low degree nodes to low degree nodes. It can be interpreted as a first order measure of the connection between nodes, i.e. the first autocorrelation of the degree–degree vector. Even though assortativity has been used so extensively, to the author’s knowledge, no attempt has been made to extend it theoretically. Indeed, Newman assortativity is about “being adjacent”, but even though two nodes may not by connected through an edge, they could have possibly a strong level of connectivity through a large number of walks and paths between them. This is the scope of our paper. We introduce, for undirected and unweighted networks, higher order assortativity by extending the Newman index based on a suitable choice of the matrix driving the connections. Higher order assortativity be defined for paths, shortest paths and random walks of a given length. The Newman assortativity is a particular case of each of these measures when the matrix is the adjacency matrix, or, in other words, the autocorrelation is of order 1. Our higher order assortativity indices help discriminating networks having the same Newman index and may reveal new topological network features. An application to airline network (Italy and US) and to Enron email network, as well as examples and simulations, are discussed.

A multiple network approach to corporate governance

In this work, we consider corporate governance (CG) ties among companies from a multiple network perspective. Such a structure naturally arises from the close interrelation between the Shareholding network and the Board of Directors network. In order to capture the simultaneous effects of both networks on CG, we propose to model the CG multiple network structure via tensor analysis. In particular, we consider the TOPHITS model, based on the PARAFAC tensor decomposition, to show that tensor techniques can be successfully applied in this context. By providing some empirical results from the Italian financial market in the univariate case, we then show that a tensor–based multiple network approach can reveal important information.

Formal and Informal Networks in Organizations

Through the study case of a restructuring process of a company, we illustrate how to detect informal networks in a company. A survey was conducted by questionnaires. We made use of eigencentrality applied to the resulting graphs. Based on the concept of hubs and authorities, we compare the informal relationships within the company with the formal structure and comment the roles and their significance.

Handbook of recent advances in commodity and financial modeling. Quantitative Methods in Banking, finance, insurance, energy and commodity markets

A widespread liberalization process in commodity and energy markets has led over the last 15 years or so to a fruitful and rich methodological spreading of techniques and quantitative approaches previously proposed in nancial markets into a wider global market area. At the same time the increasing volatility of international prices and the introduction of regulatory frameworks on banking and insurance institutions enhanced the research on risk theory and risk management inducing new, practically relevant, theoretical developments. This Handbook, at the time it was proposed to Springer, aimed at elaborating on such evidence to include contributions related to optimization, pricing and valuation problems, risk modeling and decision making problems arising in now-a-days global nancial and commodity markets from the perspective of Operations Research and Management Science.

Dynamical phase diagrams of a love capacity constrained prey–predator model

Abstract One interesting question in love relationships is: finally, what and when is the end of this love relationship? Using a prey–predator Verhulst–Lotka–Volterra (VLV) model we imply cooperation and competition tendency between people in order to describe a “love dilemma game”. We select the most simple but immediately most complex case for studying the set of nonlinear differential equations, i.e. that implying three persons, being at the same time prey and predator. We describe four different scenarios in such a love game containing either a one-way love or a love triangle. Our results show that it is hard to love more than one person simultaneously. Moreover, to love several people simultaneously is an unstable state. We find some condition in which persons tend to have a friendly relationship and love someone in spite of their antagonistic interaction. We demonstrate the dynamics by displaying flow diagrams.