An empirical study of Chinese language networks

Chinese is spoken by the largest number of people in the world, and it is regarded as one of the most important languages. In this paper, we explore the statistical properties of Chinese language networks (CLNs) within the framework of complex network theory. Based on one of the largest Chinese corpora, i.e. People’s Daily Corpus, we construct two networks (CLN1 and CLN2) from two different respects, with Chinese words as nodes. In CLN1, a link between two nodes exists if they appear next to each other in at least one sentence; in CLN2, a link represents that two nodes appear simultaneously in a sentence. We show that both networks exhibit small-world effect, scale-free structure, hierarchical organization and disassortative mixing. These results indicate that in many topological aspects Chinese language shapes complex networks with organizing principles similar to other previously studied language systems, which shows that different languages may have some common characteristics in their evolution processes. We believe that our research may shed some new light into the Chinese language and find some potentially significant implications.     

Mixing navigation on networks

In this article, we propose a mixing navigation mechanism, which interpolates between random-walk and shortest-path protocol. The navigation efficiency can be remarkably enhanced via a few routers. Some advanced strategies are also designed: For non-geographical scale-free networks, the targeted strategy with a tiny fraction of routers can guarantee an efficient navigation with low and stable delivery time almost independent of network size. For geographical localized networks, the clustering strategy can simultaneously increase efficiency and reduce the communication cost. The present mixing navigation mechanism is of significance especially for information organization of wireless sensor networks and distributed autonomous robotic systems.     

Unified index to quantifying heterogeneity of complex networks

Although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function, a unified definition of the heterogeneity of a network with any degree distribution is absent. In this paper, we define a heterogeneity index 0≤H<1 to quantify the degree heterogeneity of any given network. We analytically show the existence of an upper bound of H=0.5 for exponential networks, thus explain why exponential networks are homogeneous. On the other hand, we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0.5 if and only if its degree exponent is between 2 and 2.5. We further show that for any power law network with a degree exponent greater than 2.5, there always exists an exponential network such that both networks have the same heterogeneity index. This may help to explain why 2.5 is a critical degree exponent for some dynamic behaviors on power law networks.     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

Dynamical response to perturbation of critical Boolean networks

Boolean networks can be used as simple but general models for complex self-organizing systems. The freedom to choose different rules and structures of interactions makes this model applicable to a wide variety of complex phenomena. It is known that the damage dynamics in annealed Boolean systems should fall in the same universality class of the directed percolation model. In this work we present results about the behavior of this model at and near the critically ordered condition for both the annealed and the quenched versions of the model. Our study concentrates on the way the system responds to a small perturbation. We show that the characteristic correlation time, i.e., the time in which any memory of this perturbation is lost, diverges as one moves towards criticality. Exactly at the critical point, we observe that the time for returning to the natural state after the perturbation follows a power-law distribution. This indicates that most perturbations are quickly restored, while few events may have a global effect on the system, suggesting a mechanism that assures at the same time robustness and adaptability. The critical exponents obtained are in agreement with the values expected for the universality class of mean-field directed percolation both in the annealed and in the quenched Boolean network model. This gives further evidence that annealed Boolean networks may in certain conditions provide a good model for understanding the behavior of regulatory systems. Our results may give insight into the way real self-organizing systems respond to external stimuli, and why critically ordered systems are often observed in Nature.     

Intermolecular interactions in organofluorine aggregates probed by laser R2PI spectroscopy

Resonant Two Photon Ionization (R2PI) spectroscopy has been applied to the study of host–guest interactions in molecular clusters formed by supersonic exspansion. Here, the results of R2PI spectroscopy of the fluorinated organic molecules para and ortho-fluoro-sec-butylbenzene and their complexes with water and argon are reported and discussed. In particular, it is shown that the position of the fluorine atom on the aromatic ring influences the formation of different kind of complexes (σ versus π) with argon and water. Ab initio calculations were performed to get insight into the molecular shape and the structure of these clusters.     

Networks that optimize a trade-off between efficiency and dynamical resilience

In this Letter we study networks that have been optimized to realize a trade-off between communication efficiency and dynamical resilience. While the first is related to the average shortest pathlength, we argue that the second can be measured by the largest eigenvalue of the adjacency matrix of the network. Best efficiency is realized in star-like configurations, while enhanced resilience is related to the avoidance of short loops and degree homogeneity. Thus crucially, very efficient networks are not resilient while very resilient networks lack in efficiency. Networks that realize a trade-off between both limiting cases exhibit core-periphery structures, where the average degree of core nodes decreases but core size increases as the weight is gradually shifted from a strong requirement for efficiency and limited resilience towards a smaller requirement for efficiency and a strong demand for resilience. We argue that both, efficiency and resilience are important requirements for network design and highlight how networks can be constructed that allow for both.     

Dynamics-driven evolution to structural heterogeneity in complex networks

The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection correlations and power-law-like degree distribution. Networks with better dynamical performance are achieved if structural evolution occurs much slower than the network dynamics. Structural heterogeneity of many biological and social dynamical systems may also be driven by various dynamics-structure coupling mechanisms.     

Evolutionary construction of geographical networks with nearly optimal robustness and efficient routing properties

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property, we investigate such a design from the following viewpoints: (1) network evolution according to a spatially heterogeneous population, (2) trimodal low degrees for the tolerant connectivity against both failures and attacks, and (3) decentralized routing within short paths. Furthermore, we point out the weakened tolerance by geographical constraints on local cycles, and propose a practical strategy by adding a small fraction of shortcut links between randomly chosen nodes in order to improve the robustness to a similar level to that of the optimal bimodal networks with a larger degree for the network size N. These properties will be useful for constructing future ad hoc networks in wide-area communications.     

Communicability betweenness in complex networks

Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano [E. Estrada, N. Hatano, Phys. Rev. E 77 (2008) 036111]. Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Fréchet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a protein-protein interaction network.