Random digraphs with given expected degree sequences: A model for economic networks

Abstract

JEL classification: D85 C49 C63 E51 G21Keywords: Diversification Complex networks Credit networks Expected degree model Modularity Community structure of networks a b s t r a c t Building upon the growing interest for complex network theory, the main ambition of this paper is to contribute to a more effective application of network theory to economic phenomena, and particularly to financial networks. We depart from recent contributions on credit networks in two respects. In the first place, we constrain diversification with the out-and in-degree distribution of nodes, by adopting a suitable extension of the expected degree model for random weighted digraphs. In the second place, we focus on real networks by using this extension as null model for statistical analysis. With the help of statistical inference, we provide a rigorous answer to the following question: do real networks obey our null model? Further, we show that this answer is tightly connected to the existence of clusters or modules, as defined by Newman and Girvan (2004), within networks.

Network Calibration and Metamodeling of a Financial Accelerator Agent Based Model

“…The former case is typical of real networks, e.g. the Japanese credit market studied in Bargigli and Gallegati (2011), whose most recent data are employed in this paper, had l = 21, 811 connections over a maximum of n × m = 2, 674 × 182 = 486, 668 in 2005.…”

Finding Communities in Credit Networks

“…Alternatively, we introduce a different ensemble whose members can be labeled as binomial networks (Bargigli and Gallegati, 2011). In this ensemble the w i j are binomially distributed with parameters v (see Note 6) and p i j :…”

“…Using the linear constraints of the problem, we can obtain the following explicit solution (Bargigli and Gallegati, 2011), from which we immediately derive the expectation (3):…”

“…Of course, we expect H 0 to be rejected if µ is not too close to unity. We can employ for this task the statistical test devised in Bargigli and Gallegati (2011):…”

“…This dataset, which has been analyzed under different perspectives in previous works (De Masi et al, 2011;Fujiwara, 2009;Fujiwara and Aoyama, 2008;Bargigli and Gallegati, 2011), includes firms listed in the Japanese stock-exchange markets. Data are compiled from firms' financial statements, integrated by a survey of Nikkei Media Marketing, Inc. in Tokyo.…”