ESTIMATION OF FLUX BETWEEN INTERACTING NODES ON HUGE INTER-FIRM NETWORKS

Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics.

Production in an economy is a set of firms' activities as suppliers and customers; a firm buys goods from other firms, puts value added and sells products to others in a giant network of production. Empirical study is lacking despite the fact that the structure of the production network is important to understand and make models for many aspects of dynamics in economy. We study a nation-wide production network comprising a million firms and millions of supplier-customer links by using recent statistical methods developed in physics. We show in the empirical analysis scale-free degree distribution, disassortativity, correlation of degree to firm-size, and community structure having sectoral and regional modules. Since suppliers usually provide credit to their customers, who supply it to theirs in turn, each link is actually a creditor-debtor relationship. We also study chains of failures or bankruptcies that take place along those links in the network, and corresponding avalanche-size distribution.