Average Path Length Of Network Research Articles

Proximity in consumer network and company new products decisions

This paper examines the effects of proximity in the consumer network structure on the diffusion of firms' new products. We find that the average path length of network on new products diffusion is unrelated to consumer preferences. The average path length of consumer network decreases the efficiency of new product diffusion. But under the similar preferences of consumers, the trend of changes of consumers network average degrees and network rewiring probability are the same as the new products diffusion efficiency, and the results will be opposite under the differentiation preferences of consumers.

Sizing complex networks

Among the many features of natural and man-made complex networks the small-world phenomenon is a relevant and popular one. But, how small is a small-world network and how does it compare to others? Despite its importance, a reliable and comparable quantification of the average pathlength of networks has remained an open challenge over the years. Here, we uncover the upper (ultra-long (UL)) and the lower (ultra-short (US)) limits for the pathlength and efficiency of networks. These results allow us to frame their length under a natural reference and to provide a synoptic representation, without the need to rely on the choice for a null-model (e.g., random graphs or ring lattices). Application to empirical examples of three categories (neural, social and transportation) shows that, while most real networks display a pathlength comparable to that of random graphs, when contrasted against the boundaries, only the cortical connectomes prove to be ultra-short.

The Synchronizability and Optimized Analysis of the Hierarchical Network

A large number of research results show that the synchronizability of complex networks is closely related to the topological structure. Some typical complex network models, such as random networks, small-world networks, BA scale-free network, etc, have totally different synchronizability. In this paper, a kind of hierarchical network synchronizability of self-similar module structures was studied, with more focus on the effect of the initial size of the module and network layer to the synchronizability and further research on the problem of network synchronous optimization. The Law of Segmentation Method was employed to reduce the maximum node betweenness and the Law of Parallel Reconnection employed to improve the ability of synchronizability of complex network by reducing the average path length of networks. Meanwhile, the effectiveness of proposed methods was verified through a lot of numerically simulative experiments.

Ising model on evolution networks and its application on opinion formation

Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavorable circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated. p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.

Synchronizability of small-world networks generated from ring networks with equal-distance edge additions

This paper investigates the impact of edge-adding number m and edge-adding distance d on both synchronizability and average path length of NW small-world networks generated from ring networks via random edge-adding. It is found that the synchronizability of the network as a function of the distance d is fluctuant and there exist some d that have almost no impact on the synchronizability and may only scarcely shorten the average path length of the network. Numerical simulations on a network of Lorenz oscillators confirm the above results. This phenomenon shows that the contributions of randomly added edges to both the synchronizability and the average path length are not uniform nor monotone in building an NW small-world network with equal-distance edge additions, implying that only if appropriately adding edges when building up the NW small-word network can help enhance the synchronizability and/or reduce the average path length of the resultant network. Finally, it is shown that this NW small-world network has worse synchronizability and longer average path length, when compared with the conventional NW small-world network, with random-distance edge additions. This may be due to the fact that with equal-distance edge additions, there is only one shortcut distance for better information exchange among nodes and for shortening the average path length, while with random-distance edge additions, there exist many different distances for doing so.