Statistical analysis of gene regulatory networks reconstructed from gene expression data of lung cancer

Recently, inferring gene regulatory network from large-scale gene expression data has been considered as an important effort to understand the life system in whole. In this paper, for the purpose of getting further information about lung cancer, a gene regulatory network of lung cancer is reconstructed from gene expression data. In this network, vertices represent genes and edges between any two vertices represent their co-regulatory relationships. It is found that this network has some characteristics which are shared by most cellular networks of health lives, such as power-law, small-world behaviors. On the other hand, it also presents some features which are obviously different from other networks, such as assortative mixing. In the last section of this paper, the significance of these findings in the context of biological processes of lung cancer is discussed.     

Statistical properties of world investment networks

We have performed a detailed investigation on the world investment networks constructed from the Coordinated Portfolio Investment Survey (CPIS) data of the International Monetary Fund, ranging from 2001 to 2006. The distributions of degrees and node strengths are scale-free. The weight distributions can be well modeled by the Weibull distribution. The maximum flow spanning trees of the world investment networks possess two universal allometric scaling relations, independent of time and the investment type. The topological scaling exponent is 1.17±0.02 and the flow scaling exponent is 1.03±0.01.     

A packet routing strategy using neural networks on scale-free networks

We propose a dynamic packet routing strategy by using neural networks on scale-free networks. In this strategy, in order to determine the nodes to which the packets should be transmitted, we use path lengths to the destinations of the packets, and adjust the connection weights of the neural networks attached to the nodes from local information and the path lengths. The performances of this strategy on scale-free networks which have the same degree distribution and different degree correlations are compared to one another. Our numerical simulations confirm that this routing strategy is more effective than the shortest path based strategy on scale-free networks with any degree correlations and that the performance of our strategy on assortative scale-free networks is better than that on disassortative and uncorrelated scale-free networks.     

Traffic dynamics in scale-free networks with tunable strength of community structure

In this paper we systematically investigate the impact of community structure on traffic dynamics in scale-free networks based on local routing strategy. A growth model is introduced to construct scale-free networks with tunable strength of community structure, and a packet routing strategy with a parameter α is used to deal with the navigation and transportation of packets simultaneously. Simulations show that the maximal network capacity stands at α=−1 in the case of identical vertex capacity and monotonously decreases with the strength of community structure which suggests that the networks with fuzzy community structure (i.e., community strength is weak) are more efficient in delivering packets than those with pronounced community structure. To explain these results, the distribution of packets of each vertex is carefully studied. Our results indicate that the moderate strength of community structure is more convenient for the information transfer of real complex systems.     

Symmetry-based structure entropy of complex networks

Precisely quantifying the heterogeneity or disorder of network systems is important and desired in studies of behaviors and functions of network systems. Although various degree-based entropies have been available to measure the heterogeneity of real networks, heterogeneity implicated in the structures of networks can not be precisely quantified yet. Hence, we propose a new structure entropy based on automorphism partition. Analysis of extreme cases shows that entropy based on automorphism partition can quantify the structural heterogeneity of networks more precisely than degree-based entropies. We also summarized symmetry and heterogeneity statistics of many real networks, finding that real networks are more heterogeneous in the view of automorphism partition than what have been depicted under the measurement of degree-based entropies; and that structural heterogeneity is strongly negatively correlated to symmetry of real networks.     

Analysis of networks using generalized mutual entropies

Generalized mutual entropy is defined for networks and applied in the analysis of complex network structures. The method is tested for the case of computer simulated scale-free networks, random networks, and their mixtures. The possible applications for real network analysis are discussed.     

Statistical dynamics of early river networks

Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of a river network and the variation of probability distribution of channel lengths. The general solution of the equation is in the product form of two terms. One term is in power form and the other is in exponent form. This distribution shows a complete history of a river network evolving from its infancy to “adulthood”). The infancy is characterized by the Gaussian distribution of the channel lengths, while the adulthood is marked by a power law distribution of the channel lengths. The variation of the distribution from the Gaussian to the power law displays a gradual developing progress of the river network. The distribution of basin areas is obtained by means of Hack’s law. These provide us with new understandings towards river networks.     

Statistical properties of corporate board and director networks

The boards of directors of the largest corporations of a country together with the directors form a dense bipartite network. The board network consists of boards connected through common directors. The director network is obtained taking the directors as nodes, and a membership in the same board as a link. These networks are involved in the decision making processes relevant to the macro-economy of a country. We present an extensive and comparative analysis of the statistical properties of the board network and the director network for the first 1000 US corporations ranked by revenue (Fortune 1000) in the year 1999 and for the corporations of the Italian Stock Market. We find several common statistical properties across the data sets, despite the fact that they refer to different years and countries. This suggests an underlying universal formation mechanism which is not captured in a satisfactory way by the existent network models. In particular we find that all the considered networks are Small Worlds, assortative, highly clustered and dominated by a giant component. Several other properties are examined. The presence of a lobby in a board, a feature relevant to decision making dynamics, turns out to be a macroscopic phenomenon in all the data sets.Received: 21 February 2004, Published online: 14 May 2004PACS: 87.23.Ge Dynamics of social systems - 89.65.-s Social and economic systems - 89.65.Gh Economics, econophysics, financial markets, business and management     

Efficient packet routing strategy in complex networks

We investigate a new efficient packet routing strategy which mitigates traffic congestion on complex networks. In order to avoid congestion, we minimize the maximum betweenness, which is a measure for concentration of routing paths passing through a node in the network. Danila et al. propose a packet routing strategy in which, instead of shortest paths, they used efficient paths, which are the paths with the minimum total summations of weights assigned to nodes in the respective paths. They use a heuristic algorithm in which the weights are updated step by step by using the information of betweenness of each node in every step and the respective total summations of weights for paths through the nodes with large degrees become comparatively large. Thus passage through such nodes, where congestion almost occurs, is likely to be avoided in their algorithm. The convergence time by their algorithm is, however, quite long. In this paper, we propose a new efficient heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in the much smaller number of iteration steps for convergence than that by the algorithm of Danila et al.     

Mitigation strategies on scale-free networks against cascading failures

According to the dynamic characteristics of the cascading propagation, we introduce a mitigation mechanism and propose four mitigation methods on four types of nodes. By the normalized average avalanche size and a new measure, we demonstrate the efficiencies of the mitigation strategies on enhancing the robustness of scale-free networks against cascading failures and give the order of the effectiveness of the mitigation strategies. Surprisingly, we find that only adopting once mitigation mechanism on a small part of the overload nodes can dramatically improve the robustness of scale-free networks. In addition, we also show by numerical simulations that the optimal mitigation method strongly depends on the total capacities of all nodes in a network and the distribution of the load in the cascading model. Therefore, according to the protection strength for scale-free networks, by the distribution of the load and the protection price of networks, we can reasonably select how many nodes and which mitigation method to efficiently protect scale-free networks at the lower price. These findings may be very useful for avoiding various cascading-failure-induced disasters in the real world and for leading to insights into the mitigation of cascading failures.     

The role of syntax in complex networks: Local and global importance of verbs in a syntactic dependency network

Syntax of natural language has been the focus of linguistics for decades. The complex network theory, being one of new research tools, opens new perspectives on syntax properties of the language. Despite numerous partial achievements, some fundamental problems remain unsolved. Specifically, although statistical properties typical for complex networks can be observed in all syntactic networks, the impact of syntax itself on these properties is still unclear. The aim of the present study is to shed more light on the role of syntax in the syntactic network structure. In particular, we concentrate on the impact of the syntactic function of a verb in the sentence on the complex network structure. Verbs play the decisive role in the sentence structure (“local” importance). From this fact we hypothesize the importance of verbs in the complex network (“global” importance). The importance of verb in the complex network is assessed by the number of links which are directed from the node representing verb to other nodes in the network. Six languages (Catalan, Czech, Dutch, Hungarian, Italian, Portuguese) were used for testing the hypothesis.     

Fuzzy analysis of community detection in complex networks

A snowball algorithm is proposed to find community structures in complex networks by introducing the definition of community core and some quantitative conditions. A community core is first constructed, and then its neighbors, satisfying the quantitative conditions, will be tied to this core until no node can be added. Subsequently, one by one, all communities in the network are obtained by repeating this process. The use of the local information in the proposed algorithm directly leads to the reduction of complexity. The algorithm runs in O(n+m) time for a general network and O(n) for a sparse network, where n is the number of vertices and m is the number of edges in a network. The algorithm fast produces the desired results when applied to search for communities in a benchmark and five classical real-world networks, which are widely used to test algorithms of community detection in the complex network. Furthermore, unlike existing methods, neither global modularity nor local modularity is utilized in the proposal. By converting the considered problem into a graph, the proposed algorithm can also be applied to solve other cluster problems in data mining.     

Semantic networks based on titles of scientific papers

In this paper we study the topological structure of semantic networks based on titles of papers published in scientific journals. It discusses its properties and presents some reflections on how the use of social and complex network models can contribute to the diffusion of knowledge. The proposed method presented here is applied to scientific journals where the titles of papers are in English or in Portuguese. We show that the topology of studied semantic networks are small-world and scale-free.     

Statistical properties of weighted complex networks characterized by metaweights

We propose several characterizations of weighted complex networks by incorporating the concept of metaweight into the clustering coefficient, degree correlation, and module decomposition. These incorporations make it possible to describe weighted networks depending on how strongly we emphasize weights. Using some applications to real-world weighted networks, we demonstrate that the proposed approach provides rich information that was inaccessible by previous analyses such as the degree correlation for a specific magnitude of weights or the community structure under controlling the importance of roles of the topology and weights.     

Response of scale-free networks with community structure to external stimuli

The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint.     

Topology identification of weighted complex dynamical networks

Recently, various papers investigated the geometry features, synchronization and control of complex network provided with certain topology. While, the exact topology of a network is sometimes unknown or uncertain. Using Lyapunov theory, we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model. By receiving the network nodes evolution, the topology of such kind of network with identical or different nodes, or even with switching topology can be monitored. Experiments show that the methods presented in this paper are of high accuracy with good performance.     

Statistical mechanics of networks: Estimation and uncertainty

Exponential random graph models (ERGMs) are powerful tools for formulating theoretical models of network generation or learning the properties of empirical networks. They can be used to construct models that exactly reproduce network properties of interest. However, tuning these models correctly requires computationally intractable maximization of the probability of a network of interest—maximum likelihood estimation (MLE). We discuss methods of approximate MLE and show that, though promising, simulation based methods pose difficulties in application because it is not known how much simulation is required. An alternative to simulation methods, maximum pseudolikelihood estimation (MPLE), is deterministic and has known asymptotic properties, but standard methods of assessing uncertainty with MPLE perform poorly. We introduce a resampling method that greatly outperforms the standard approach to characterizing uncertainty with MPLE. We also introduce ERGMs for dynamic networks—temporal ERGM (TERGM). In an application to modeling cosponsorship networks in the United States Senate, we show how recently proposed methods for dynamic network modeling can be integrated into the TERGM framework, and how our resampling method can be used to characterize uncertainty about network dynamics.     

Complex networks constructed from irrational number sequences

In this paper, we construct (d,r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r=0,1,…,d−1), and the undirected edges indicate the adjacency between two consecutive groups. (3,r) and (4,r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.     

Evolution of Chinese airport network

With the rapid development of the economy and the accelerated globalization process, the aviation industry plays a more and more critical role in today’s world, in both developed and developing countries. As the infrastructure of aviation industry, the airport network is one of the most important indicators of economic growth. In this paper, we investigate the evolution of the Chinese airport network (CAN) via complex network theory. It is found that although the topology of CAN has remained steady during the past few years, there are many dynamic switchings inside the network, which have changed the relative importance of airports and airlines. Moreover, we investigate the evolution of traffic flow (passengers and cargoes) on CAN. It is found that the traffic continues to grow in an exponential form and has evident seasonal fluctuations. We also found that cargo traffic and passenger traffic are positively related but the correlations are quite different for different kinds of cities.     

Detecting the optimal number of communities in complex networks

To obtain the optimal number of communities is an important problem in detecting community structures. In this paper, we use the extended measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic Ω(c) is proposed to detect the optimal number of communities. In general, when Ω(c) reaches its local maximum, especially the first one, the corresponding number of communities c is likely to be optimal in community detection. Moreover, the statistic Ω(c) can also measure the significance of community structures in complex networks, which has been paid more attention recently. Numerical and empirical results show that the index Ω(c) is effective in both artificial and real world networks.