arXiv subjects

Massimo Riccaboni

Publications and source records attributed to Massimo Riccaboni.

45 records · Page 3Linked to original sources

arXiv2012

Global Networks of Trade and Bits

Considerable efforts have been made in recent years to produce detailed topologies of the Internet. Although Internet topology data have been brought to the attention of a wide and somewhat diverse audience of scholars, so far they have been overlooked by economists. In this paper, we suggest that such data could be effectively treated as a proxy to characterize the size of the "digital economy" at country level and outsourcing: thus, we analyse the topological structure of the network of trade in digital services (trade in bits) and compare it with that of the more traditional flow of manufactured goods across countries. To perform meaningful comparisons across networks with different characteristics, we define a stochastic benchmark for the number of connections among each country-pair, based on hypergeometric distribution. Original data are thus filtered by means of different thresholds, so that we only focus on the strongest links, i.e., statistically significant links. We find that trade in bits displays a sparser and less hierarchical network structure, which is more similar to trade in high-skill manufactured goods than total trade. Lastly, distance plays a more prominent role in shaping the network of international trade in physical goods than trade in digital services.

physics.soc-ph↗

arXiv2009

The Structure and Growth of Weighted Networks

We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by assuming that link weights evolve according to a geometric Brownian motion. Our model is verified by means of simulations and real world trade data. We show that the model correctly predicts the intensity and growth distribution of links, the size-variance relationships of the growth of link weights, the relationship between the degree and strength of nodes, as well as the scale-free structure of the network.

q-fin.GN↗

arXiv2009

The Size Variance Relationship of Business Firm Growth Rates

The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $σ(S) \sim S^{-β(S)}$ where $S$ is the firm size and $β(S)\approx 0.2$ is an exponent weakly dependent on $S$. Here we show how a model of proportional growth which treats firms as classes composed of various number of units of variable size, can explain this size-variance dependence. In general, the model predicts that $β(S)$ must exhibit a crossover from $β(0)=0$ to $β(\infty)=1/2$. For a realistic set of parameters, $β(S)$ is approximately constant and can vary in the range from 0.14 to 0.2 depending on the average number of units in the firm. We test the model with a unique industry specific database in which firm sales are given in terms of the sum of the sales of all their products. We find that the model is consistent with the empirically observed size-variance relationship.

q-fin.ST↗

arXiv2008

Structure of Business Firm Networks and Scale-Free Models

We study the structure of business firm networks and scale-free models with degree distribution $P(q) \propto (q+c)^{-λ}$ using the method of $k$-shell decomposition.We find that the Life Sciences industry network consist of three components: a ``nucleus,'' which is a small well connected subgraph, ``tendrils,'' which are small subgraphs consisting of small degree nodes connected exclusively to the nucleus, and a ``bulk body'' which consists of the majority of nodes. At the same time we do not observe the above structure in the Information and Communication Technology sector of industry. We also conduct a systematic study of these three components in random scale-free networks. Our results suggest that the sizes of the nucleus and the tendrils decrease as $λ$ increases and disappear for $λ\geq 3$. We compare the $k$-shell structure of random scale-free model networks with two real world business firm networks in the Life Sciences and in the Information and Communication Technology sectors. Our results suggest that the observed behavior of the $k$-shell structure in the two industries is consistent with a recently proposed growth model that assumes the coexistence of both preferential and random agreements in the evolution of industrial networks.

physics.soc-ph↗

arXiv2007

Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution $P(C)\sim C^{-δ}$. We find that for non-fractal scale-free networks $δ= 2$, and for fractal scale-free networks $δ= 2-1/d_{B}$, where $d_{B}$ is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at AS level (N=20566), where $N$ is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length $\ell^{*}$, separating fractal and non-fractal regimes, scales with dimension $d_{B}$ of the network as $p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.

physics.soc-ph↗

arXiv2006

A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $ζ=3$. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.

physics.data-an↗

arXiv2005

The Growth of Business Firms: Theoretical Framework and Empirical Evidence

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the model's predictions agree with empirical growth distributions and size-variance relationships.

physics.data-an↗

arXiv2005

A Generalized Preferential Attachment Model for Complex Systems

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry.

physics.soc-ph↗

arXiv2005

Statistical Properties of Business Firms Structure and Growth

We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent $β= 0.20 \pm 0.01$. We also find that the average sales of products scales with the firm sales as a power law with exponent $α= 0.57 \pm 0.02$. And that the average number products of a firm scales with the firm sales as a power law with exponent $γ= 0.42 \pm 0.02$. We compare these findings with the predictions of models proposed till date on growth of business firms.

physics.soc-ph↗