Rosanna Grassi

The Economic Effect of Interlocking Directorates in Italy: New Evidence Using Centrality Measures

We use measures of vertex centrality to examine interlocking directorates and their economic effects in Italy. We employ centrality measures like degree, eigenvector centrality, betweenness, and flow betweenness, along with the clustering coefficient. We document the existence of a negative relationship between both degree and eigenvector centrality and firm value. Betweenness and flow betweenness, on the other hand, are not associated with lower firm valuations. We argue that these differences derive from the different properties of these measures: while degree and eigenvector centrality measures the influence and the power of the connections, betweenness and flow betweenness are proxies for the volume of information that passes between the nodes. This result is robust with respect to the use of both stock market and operating performance measures, as well as several controlling variables.

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.

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.

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.

Market Dynamics When Agents Anticipate Correlation Breakdown

The aim of this paper is to analyse the effect introduced in the dynamics of a financial market when agents anticipate the occurrence of a correlation breakdown. What emerges is that correlation breakdowns can act both as a consequence and as a triggering factor in the emergence of financial crises rational bubbles. We propose a market with two kinds of agents: speculators and rational investors. Rational agents use excess demand information to estimate the variance-covariance structure of assets returns, and their investment decisions are represented as a Markowitz optimal portfolio allocation. Speculators are uninformed agents and form their expectations by imitative behavior, depending on market excess demand. Several market equilibria result, depending on the prevalence of one of the two types of agents. Differing from previous results in the literature on the interaction between market dynamics and speculative behavior, rational agents can generate financial crises, even without the speculator contribution.

Directed clustering in weighted networks: A new perspective

Abstract Several definitions of clustering coefficient for weighted networks have been proposed in literature, but less attention has been paid to both weighted and directed networks. We provide a new local clustering coefficient for this kind of networks, starting from those already existing in the literature for the weighted and undirected case. Furthermore, we extract from our coefficient four specific components, in order to separately consider different link patterns of triangles. Empirical applications on several real networks from different frameworks and with different order are provided. The performance of our coefficient is also compared with that of existing coefficients.

Measuring Structural Dissimilarity Between Finite Partial Orders

In this paper, we address the problem of measuring structural dissimilarity between two partial orders with n elements. We propose a structural dissimilarity measure, based on the distance between isomorphism classes of partial orders, and propose an interpretation in terms of graph theory. We give examples of structural dissimilarity computations, using a simulated annealing algorithm for numerical optimization.

Equilibrium Prices on a Financial Graph

The analysis of financial markets usually assumes that trades are centralized and open to all investors. Investors are typically price takers. A relatively recent interest has been devoted to local markets open to a limited number of traders. Such markets may be fruitfully analyzed by means of graphs where traders are the nodes and trades are the arcs. In this model one bilateral trade occurs each round. Agents are risk averse and act myopically seeking to maximize their expected utility. Conditions for the agents to trade and to find an equilibrium price are determined theoretically. An ad-hoc algorithm is applied to find a numerical solution and to simulate the path toward the equilibrium price depending on different initial settings.

Does Expectation of Correlation Breakdown in Financial Market Fulfill Itself

This paper develops a model appeared in the literature whose focus was the way rational risk averse investors anticipate the correlation breakdowns of asset returns in periods of excess demand. That model analysed the dynamics of the “expected” returns of the risky asset, and their consistency with empirical evidence. However, the same model did not provide any evidence on actual correlation generated by the dynamics of returns. A model to link asset returns to excess demand is required to analyse the implied correlation between the securities traded. In this work we estimate such a model. Results confirm that the expected and ex-post correlation tend to move closely. In other words a self-fulfilling prophecy about correlation breakdown can take place, even when rational agents dominate the financial market.