Xu Cai

The effect of interdependence on the percolation of interdependent networks

Abstract Two stochastic models are proposed to generate a system composed of two interdependent scale-free (SF) or Erdős–Renyi (ER) networks where interdependent nodes are connected with an exponential or power-law relation, as well as different dependence strength, respectively. Each subnetwork grows through the addition of new nodes with constant accelerating random attachment in the first model but with preferential attachment in the second model. The two subnetworks interact with multi-support and undirectional dependence links. The effects of dependence relations and strength between subnetworks are analyzed in the percolation behavior of fully interdependent networks against random failure, both theoretically and numerically, and as a result, for both relations: interdependent SF networks show a second-order percolation phase transition and the increased dependence strength decreases the robustness of the system, whereas, interdependent ER networks show the opposite results. In addition, the power-law relation between networks yields greater robustness than the exponential one at the given dependence strength.

The dependence of graph energy on network structure

In this paper, we aim at investigating how the energy of a graph depends upon its underlying topological structure for regular and sparse scale free networks. Firstly, the spectra and energies of some simple regular graphs are calculated exactly and an exact expression is derived for the eigenvalues of adjacency matrix of regular graphs with degree k being given by k = 2a (a = 1, 2, 3,...). It is also found that a graph with k being about 0.8N owns the largest energy for the regular graphs with the same size and the same generating method used in this paper. Furthermore, we investigate the energy of sparse scale-free networks with different average degree and degree distribution exponent γ. While γ is specified, the energy is a power-law function of with exponent being about 0.5. And while is fixed, energy will be obviously proportional to γ. Otherwise, we also find that the energy is a power- law function of the variance of degree sequence with exponent weakly depending on the size of network. Interestingly, while both and γ are specified, there will be a terrific linear fit to the relationship between energy and the size of system.

Network Aggregation Process in Multilayer Air Transportation Networks

The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network (CATN) as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.

A simple phenomenological model for time evolution of social networks

Inspired by the maxim long union divides and long division unites, a phenomenological model with the simplification of real social networks is proposed to explore the evolutionary features of these networks composed of the entities whose behaviors are dominated by two events: union and division. The nodes are endowed with some attributes such as identity, ingredient, richness, age and internal diversity, which determine collectively the evolution in a probabilistic way. Through the local interaction of two events, a stationary state of network is reached as a constant amount of nodes survive with no more event happened in the network, like a situation of tripartite confrontation. Besides, the number of survived nodes and the speed of network evolution can be controlled by two parameters.

Recent Progress in Some Active Topics on Complex Networks

Complex networks have been extensively studied across many fields, especially in interdisciplinary areas. It has since long been recognized that topological structures and dynamics are important aspects for capturing the essence of complex networks. The recent years have also witnessed the emergence of several new elements which play important roles in network study. By combining the results of different research orientations in our group, we provide here a review of the recent advances in regards to spectral graph theory, opinion dynamics, interdependent networks, graph energy theory and temporal networks. We hope this will be helpful for the newcomers of those fields to discover new intriguing topics.