Family Of Small-world Networks Research Articles

An Analysis of Shipping Agreements: The Cooperative Container Network

The recent economic downturn has intensified the need for cooperation among carriers in the container shipping industry. Indeed, carriers join inter-firm networks for several reasons such as achieving economies of scale, scope, and the search for new markets. In this paper we apply network analysis and construct the Cooperative Container Network in order to study how shipping companies integrate and coordinate their activities and to investigate the topology and hierarchical structure of inter-carrier relationships. Our data set is comprised of 65 carriers that provide 603 container services. The results indicate that the Cooperative Container Network (CCN) belongs to the family of small world networks. This finding suggests that the most cooperative companies are small-to-medium-size carriers that engage in commercial agreements in order to reduce costs and, when in partnership with larger carriers, these cooperative companies are able to compete, especially against the largest carriers. However shipping companies with high capacity engage in cooperation with other carriers by merely looking for local partners in order to increase their local and specialized market penetration.

SYNCHRONIZATION IN THE FAMILY OF CHAOTIC SMALL-WORLD NETWORKS

In this paper we investigate by computer simulation the synchronizability of the family of small-world networks, which consists of identical chaotic units, such as the Lorenz chaotic system, the Chen chaotic system, Lü chaotic system, and the unified chaotic system (unit). It is shown that for weak coupling, synchronization clusters emerge in the networks whose disorder probabilities p are large but do not emerge in the networks whose disorder probabilities p are small; while for strong coupling under which the regular networks do not exhibit synchronization, all dynamical nodes, behaving as in the random networks, mutually synchronize in the networks which own very small disorder probability p and have both high degree of clustering and small average distance. Based on the concepts of clustering coefficient C(p), characteristic path length L(p) and global efficiency E(G), these phenomena are discussed briefly.

Random spread on the family of small-world networks.

We present analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from regular to random behavior with increasing distance from the starting point of the random walk. We introduce an independent step approximation, which enables us to obtain analytic results for the average access time. We observe a scaling relation for the average access time in the degree of the nodes. The behavior of the average access time as a function of p shows striking similarity with that of the characteristic length of the graph. This observation may have important applications in routing and switching in networks with a large number of nodes.