Scale-free Degree Distribution Research Articles

Dynamical Topology Analysis Of Vanet Based On Complex Networks Theory

Abstract A Vehicular Ad hoc NETwork (VANET) is a special subset of multi-hop Mobile Ad hoc Networks, in which the vehicles wireless interfaces can communicate with each other, as well as with fixed equipments alongside city roads or highways. Vehicular mobility dynamic characteristics, including high speed, predictable, restricted mobility pattern significantly affect the performance of routing protocols in a real VANET. Based on the existing studies, here we propose a testing network according to the preferential attachment on the degree of nodes and analyze VANET model characteristics for finding out the dynamic topology from the instantaneous degree distribution, instantaneous clustering coefficient and average path length. Analysis and simulation results demonstrate that VANET has a small world network features and is characterized by a truncated scale-free degree distribution with power-law degree distribution. The dynamic topology analysis indicates a possible mechanism of VANET, which might be helpful in the traffic congestion, safety and management.

Abstract 363: Planar filtered gene regulatory networks in breast cancer

Abstract Gene co-expression network analysis has been shown to be effective in identifying functional co-expressed gene modules associated with complex human diseases such as cancer, Alzheimers’ disease, obesity and diabetes. However, existing techniques to construct co-expression networks require some critical prior information such as predefined number of modules to be detected and numerical thresholds for defining coexpression/interaction, or do not naturally reproduce the hallmarks of complex systems such as scale-free degree distribution of small-worldness). In order to mitigate these problems as whole or in part, we have developed a novel co-expression network analysis approach, Planar Filtered Network Analysis (PFNA). PFNA utilizes a graph filtering technique to identify “true” interactions by means of embedding candidate interactions on a topological sphere(2, 3). Planar Filtered Networks (PFN) are naturally scale-free, small-world, and are comprised of a number of highly co-expressed gene modules). Furthermore, PFNA allows differential topology analysis of networks from different disease states based on centrality and peripherality metrics). We performed PFNA on the breast cancer data from The Cancer Genome Atlas (TCGA), and identified a number of novel gene modules associated with overall survival of the whole cohort or patient subgroups defined by receptor status (ER, PR, HER2) and PAM50 biomarkers(6). PFNA uncovers not only gene modules enriched for genes in well-known cancer pathways such as cell-cycle and immune response, but also novel modules that prognostically stratify patients with triple negative or basal breast cancers. Notably, several modules involved in G-protein coupled receptor signaling, protocadherin α and β pathways are highly predictive of survival for patients with triple negative disease. Furthermore, the differential topology analysis reveals that breast cancer biomarkers such as PAM50 and poor prognosis gene sets developed by van’t Veer et al(7) are more central in the tumor network than the one based on the matched adjacent normal breast tissues. In summary, PFNA reveals a number of novel high-level molecular features of the highly heterogeneous breast cancer. This novel network analysis method provides a set of unsupervised tools to objectively identify subnetworks that are associated with complex diseases such as breast cancer. 1. R. Albert, A. L. Barabasi. Rev Mod Phys 74, 47. 2. M.Tumminello, T. Aste, T. Di Matteo, R. N. Mantegna. Proc Natl Acad Sci U S A 102,10421. 3. T.Aste, T. Di Matteo, S. T. Hyde. Physica A 346, 20. 4. W.M. Song, T. Di Matteo, T. Aste. Phys RevE Stat Nonlin Soft Matter Phys 85,046115. 5. F.Pozzi, T. Di Matteo, T. Aste. Adv Complex Syst 11, 927. 6. J. S. Parker et al.. Journal of clinical oncology: 27, 1160. 7. L.J. van 't Veer et al.. Nature 415, 530. Citation Format: Won-min Song, Tao Huang, Seungyeul Yoo, EunJee Lee, Yongzhong Zhao, Li Wang, Zhidong Tu, Xudong Dai, Hanna Irie, Jun Zhu, Bin Zhang. Planar filtered gene regulatory networks in breast cancer. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 363. doi:10.1158/1538-7445.AM2014-363

Systemic risk in banking networks: Advantages of “tiered” banking systems

This paper studies the risk and potential impact of system-wide defaults in a tiered banking network, where a small group of head institutions has many credit linkages with other banks, while the majority of banks have only a few links. A network is random and displays a given distribution of the number of banks׳ linkages, known as degree. We model tiering by a negative correlation between degrees of neighboring banks and by a scale-free degree distribution. The main findings of the paper highlight the advantages of tiering. Both the risk of systemic crisis and the potential scope of the crisis are lower in systems with negative correlation of bank degrees than in other types of systems. Similarly, in scale-free networks, the resilience of the system to shocks is increasing with the level of tiering.

Functional brain networks formed using cross-sample entropy are scale free.

Over the previous decade, there has been an explosion of interest in network science, in general, and its application to the human brain, in particular. Most brain network investigations to date have used linear correlations (LinCorr) between brain areas to construct and then interpret brain networks. In this study, we applied an entropy-based method to establish functional connectivity between brain areas. This method is sensitive to both nonlinear and linear associations. The LinCorr-based and entropy-based techniques were applied to resting-state functional magnetic resonance imaging data from 10 subjects, and the resulting networks were compared. The networks derived from the entropy-based method exhibited power-law degree distributions. Moreover, the entropy-based networks had a higher clustering coefficient and a shorter path length compared with that of the LinCorr-based networks. While the LinCorr-based networks were assortative, with nodes with similar degrees preferentially connected, the entropy-based networks were disassortative, with high-degree hubs directly connected to low-degree nodes. It is likely that the differences in clustering and assortativity are due to "mega-hubs" in the entropy-based networks. These mega-hubs connect to a large majority of the nodes in the network. This is the first work clearly demonstrating differences between functional brain networks using linear and nonlinear techniques. The key finding is that the nonlinear technique produced networks with scale-free degree distributions. There remains debate among the neuroscience community as to whether human brains are scale free. These data support the argument that at least some aspects of the human brain are perhaps scale free.

Random complex networks

AbstractExactly what is meant by a ‘complex’ network is not clear; however, what is clear is that it is something other than a random graph. Complex networks arise in a wide range of real social, technological and physical systems. In all cases, the most basic categorization of these graphs is their node degree distribution. Particular groups of complex networks may exhibit additional interesting features, including the so-called small-world effect or being scale-free. There are many algorithms with which one may generate networks with particular degree distributions (perhaps the most famous of which is preferential attachment). In this paper, we address what it means to randomly choose a network from the class of networks with a particular degree distribution, and in doing so we show that the networks one gets from the preferential attachment process are actually highly pathological. Certain properties (including robustness and fragility) which have been attributed to the (scale-free) degree distribution are actually more intimately related to the preferential attachment growth mechanism. We focus here on scale-free networks with power-law degree sequences—but our methods and results are perfectly generic.

The network structure of the CDS market and its determinants

This paper analyses the network structure of the credit default swap (CDS) market and its determinants, using a unique dataset of bilateral notional exposures on 642 financial and sovereign reference entities. We find that the CDS network is centred around 14 major dealers, exhibits a “small world” structure and a scale-free degree distribution. A large share of investors are net CDS buyers, implying that total credit risk exposure is fairly concentrated. Consistent with the theoretical literature on the use of CDS, the debt volume outstanding and its structure (maturity and collateralization), the CDS spread volatility and market beta, as well as the type (sovereign/financial) of the underlying bond are statistically significantly related—with expected signs—to structural characteristics of the CDS market.

Opinion formation of free speech on the directed social network

A dynamical model with continuous opinion is proposed to study how the speech order and the topology of directed social network affect the opinion formation of free speech. In the model, agents express their opinions one by one with random order (RO) or probability order (PO), other agents paying attentions to the speaking agent, receive provider's opinion, update their opinions and then express their new opinions in their turns. It is proved that with the same agent j repeats its opinion more, other agents who pay their attentions to j and include j's opinion in their confidence level at initial time, will continue approaching j's opinion. Simulation results reveal that on directed scale-free network: (1) the model for PO forms fewer opinion clusters, larger maximum cluster (MC), smaller standard deviation (SD), and needs less waiting time to reach a middle level of consensus than RO; (2) as the parameter of scale-free degree distribution decreases or the confidence level increases, the results often get better for both speech orders; (3) the differences between PO and RO get smaller as the size of network decreases.

Epidemic spreading on dynamical networks with temporary hubs and stable scale-free degree distribution

Recent empirical analyses of some realistic dynamical networks have demonstrated that their degree distributions are stable scale-free (SF), but the instantaneous well-connected hubs at one point of time can quickly become weakly connected. Motivated by these empirical results, we propose a simple toy dynamical agent-to-agent contact network model, in which each agent stays at one node of a static underlay network and the nearest neighbors swap their positions with each other. Although the degree distribution of the dynamical network model at any one time is equal to that in the static underlay network, the numbers and identities of each agent’s contacts will change over time. It is found that the dynamic interaction tends to suppress epidemic spreading in terms of larger epidemic threshold, smaller prevalence (the fraction of infected individuals) and smaller velocity of epidemic outbreak. Furthermore, the dynamic interaction results in the prevalence to undergo a phase transition at a finite threshold of the epidemic spread rate in the thermodynamic limit, which is in contradiction to the absence of an epidemic threshold in static SF networks. Some of these findings obtained from heterogeneous mean-field theory are in good agreement with numerical simulations.

Duality between preferential attachment and static networks on hyperbolic spaces

There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate scale-free networks. We show that there is actually a duality between a class of growing spatial networks based on preferential attachment on the sphere and a class of static random networks on the hyperbolic plane. Both classes of networks have the same scale-free degree distribution as the Barabasi-Albert model. As a limit of this correspondence, the Barabasi-Albert model is equivalent to a static random network on an hyperbolic space with infinite curvature.

Hidden Social Networks that Drive Online Public Involvement in Infrastructure Construction

Several studies have emphasized the role of social media in public involvement during planning, construction, and operation of infrastructure. Social media can offer optimal, bidirectional communication with the public and an efficient flow of information and feedback between decision makers and project end users. However, the underlying social networks formed in the background of public relations processes on online social media largely have been neglected. Such networks are referred to as infrastructure discussion networks (IDN) and can be rich sources of information for decision makers. If it can be proved that these networks follow the general behavior of social networks, then rich tools developed in social network analysis can be used to profile users and help decision makers study user attitudes. This paper compares the IDNs of four light rail transit projects in various cities in the United States and Canada and studies them under the microscope of social network analysis. The study shows that IDNs exhibit the general structure of social networks (such as small-world behavior, scale-free degree distribution, and high clustering). The IDNs also include meaningful communities, detection and evaluation of which could lead to more efficient offline and online public involvement processes. Given the recent trends in presence of infrastructure projects on online social media, the methods presented in this paper can be readily applied by practitioners to improve their public engagement practices.

Contextualized Analysis of Social Networks: Collaboration in Scientific Communities

Currently, the collaboration in scientific communities has been studied in order to explain, among other things, the knowledge diffusion. The quality of Graduate Programmes is often associated with the scientific collaboration. This paper discusses how scientific collaboration processes can be identified and characterized through social and complex networks. For this purpose, collaboration networks of bibliographic production, research projects, and committees of PhD theses and Masters’ dissertations by researchers from a graduate program in computational modeling were studied. The data were obtained from CAPES’ reports of the period from 2001 to 2009. Among the studied indices, centrality indices indicate the presence of prominent researchers who influence others and promptly interact with other researchers in the network. The indices of complex networks reveal the presence of the small-world (i.e. these networks are favorable to increase coordination between researchers) phenomenon and indicate a behavior of scale-free degree distribution (i.e. some researchers promote clustering more than others) for one of the studied networks.

S-core network decomposition: A generalization ofk-core analysis to weighted networks

A broad range of systems spanning biology, technology, and social phenomena may be represented and analyzed as complex networks. Recent studies of such networks using k-core decomposition have uncovered groups of nodes that play important roles. Here, we present s-core analysis, a generalization of k-core (or k-shell) analysis to complex networks where the links have different strengths or weights. We demonstrate the s-core decomposition approach on two random networks (ER and configuration model with scale-free degree distribution) where the link weights are (i) random, (ii) correlated, and (iii) anticorrelated with the node degrees. Finally, we applythes-core decomposition approach to the protein-interaction network of the yeast Saccharomyces cerevisiaeinthe context of two gene-expression experiments: oxidative stress in response to cumene hydroperoxide (CHP), and fermentation stress response (FSR). We find that the innermost s-cores are (i) different from innermost k-cores, (ii) different for the two stress conditions CHP and FSR, and (iii) enriched with proteins whose biological functions give insight into how yeast manages these specific stresses.

Structural features beneath neuronal avalanches

Recently, Friedman et al performed high-resolution measurements [1] that strongly supported an universal critical character (in the sense of statistical physics) of neuronal avalanches, despite the abnormally high frequency of large events (bumps in the distributions of size and lifetime of avalanches) deforming the pure power-law behavior expected from analogies to equilibrium critical phenomena that became manifest only for smaller events. Based on simulations of the Kinouchi-Copelli (KC) model, we have shown [2] that such bumps may not be experimental artifacts and really be typical at criticality when the topology of the neural network is the Barabasi-Albert (BA) model, leading to a scale-free degree distribution of exponent -3.0. On the other hand, those simulations could not reproduce the exponents of the power-law region of the avalanche distributions in [1] (namely, -1.7 for the size distribution and -1.9 for the lifetime distribution). Besides that, the KC dynamics on BA topology revealed that the information capacity (entropy of avalanche size distribution) did not exhibit critical optimization, in contrast with an earlier experiment [3]. In this study we investigate the KC dynamics on the Uncorrelated Configuration Model (UCM) [4]. The UCM is a kind of wiring procedure of a neural topology that can lead to scale-free degree distributions with tunable exponents and can be matched to BA model. However, even so their avalanches are not identical. While the UCM also allows the appearance of bumps on the avalanche distributions, it both shows that the information capacity may be critically optimal and exhibits quantitatively accurate values of the critical exponents for small avalanches, suggesting the UCM may be descriptive of some structural features in the systems claimed to exhibit critical dynamics.

The protein–protein interaction network of the human Sirtuin family

Protein–protein interaction networks are useful for studying human diseases and to look for possible health care through a holistic approach. Networks are playing an increasing and important role in the understanding of physiological processes such as homeostasis, signaling, spatial and temporal organizations, and pathological conditions. In this article we show the complex system of interactions determined by human Sirtuins (Sirt) largely involved in many metabolic processes as well as in different diseases. The Sirtuin family consists of seven homologous Sirt-s having structurally similar cores but different terminal segments, being rather variable in length and/or intrinsically disordered. Many studies have determined their cellular location as well as biological functions although molecular mechanisms through which they act are actually little known therefore, the aim of this work was to define, explore and understand the Sirtuin-related human interactome. As a first step, we have integrated the experimentally determined protein–protein interactions of the Sirtuin-family as well as their first and second neighbors to a Sirtuin-related sub-interactome. Our data showed that the second-neighbor network of Sirtuins encompasses 25% of the entire human interactome, and exhibits a scale-free degree distribution and interconnectedness among top degree nodes. Moreover, the Sirtuin sub interactome showed a modular structure around the core comprising mixed functions. Finally, we extracted from the Sirtuin sub-interactome subnets related to cancer, aging and post-translational modifications for information on key nodes and topological space of the subnets in the Sirt family network.

Community Detecting and Feature Analysis in Real Directed Weighted Social Networks

Real social networks usually have some structural features of the complex networks, such as community structure, the scale-free degree distribution, clustering, small world network, dynamic evolution and so on. A new community detecting algorithm for directed and weighted social networks is proposed in this paper. Due to the use of more reference information, the accuracy of the algorithm is better than some of the typical detecting algorithms. And because of the use of heap structure and multi-task modular architecture, the algorithm also got a high computational efficiency than other algorithms. The effectiveness and efficiency of the algorithm is validated by experiments on real social networks. Based on the theories and models of complex networks, the features of the real large social networks are analyzed.

Modeling and navigation of social information networks in metric spaces

We are living in a world of various kinds of social information networks with small-world and scale-free characteristics. It is still an intriguing problem for researchers to explain how and why so many obviously different networks emerge and share common intrinsic characteristics such as short diameter, higher cluster and power-law degree distribution. Most previous works studied the topology formation and information navigation of complex networks in separated models. In this paper, we propose a metric based range intersection model to explore the topology evolution and information navigation in a synthetic way. We model the network as a set of nodes in a distance metric space where each node has an ID and a range of neighbor information around its ID in the metric space. The range of a node can be seen as the local knowledge or information that the node has around its position in the metric space. The topology is formed by setting up a link between two nodes that have intersected ranges. Information navigation over the network is modeled as a greedy routing process using neighbor links and the distance metric. Different from previous models, we do not assume that nodes join the network one by one and set up link according to the degree distribution of existing nodes or distances between nodes. Range of node is the key factor determining the topology and navigation properties of a network. Moreover, as the ranges of nodes grow, the network evolves from a set of totally isolated nodes to a connected network. Thus, we can easily model the network evolutions in terms of the network size and the individual node information range using the range intersection model. A set of experiments shows that networks constructed using the range intersection model have the scale-free degree distribution, high cluster, short diameter, and high navigability properties that are owned by the real networks.

The procedure of evolution modelling of biochemical networks structure

The exploration of biochemical networks, such as gregulation, metabolic, protein interaction and signal transduction networks helps to understand better ce llular processes, properties and functions of biolo gical system. An important task of biological systems investigation is explora tion of biochemical networks evolution and dynamic changes of their structure under pressure of the mutations and natural selecti on that are mentioned as the main evolution forces. Proposed network growth models have been used to establish topological prop erties of biochemical networks, such as scale-free degree distribution, ultra- small-world property, centrality and modularity. Bu t they consider network evolution implicitly, gener ally and ignore important properties of biological systems. To demonstrate an d investigate the evolution course of biochemical n etworks structure caused by genetic mutations, chosen by natural selection and depending of the biological system properties, evol ution models are needed what takes into account these features. In this pap er evolution modelling procedure is introduced as w ell as algorithm of biochemical networks structure that occurs as a res ult of genetic alterations by pressure of natural sand takes into account different importance levels of biochemical processe s.

Modeling the dynamics of infectious diseases in different scale-free networks with the same degree distribution

Abstract The transmission dynamics of some infectious diseases is related to the contact structure between individuals in a network. We used five algorithms to generate contact networks with different topological structure but with the same scale-free degree distribution. We simulated the spread of acute and chronic infectious diseases on these networks, using SI (Susceptible – Infected) and SIS (Susceptible – Infected – Susceptible) epidemic models. In the simulations, our objective was to observe the effects of the topological structure of the networks on the dynamics and prevalence of the simulated diseases. We found that the dynamics of spread of an infectious disease on different networks with the same degree distribution may be considerably different.

Measuring degree-dependent failure in scale-free networks of bipartite structure

We study degree-dependent failure in networks consisting of two types of nodes with edges running only between nodes of unlike type. Both types of nodes are assumed to have scale-free degree distributions. These networks are called scale-free bipartite graphs, which appear in many real-life networks. In this article, we measure network robustness and fragility based on a recently proposed spectral measure, natural connectivity, which is an average eigenvalue obtained from the graph spectrum. During the edge removal process, an edge between nodes with degrees k and l is retained with a probability proportional to (kl) –α, where α > 0 is a biased exponent, so that the most connected nodes are depreciated first. A clear division between robust regime and fragile regime can be extracted based on natural connectivity by tuning the exponent α. The theory is verified by the numerical simulations.

The Network Structure of the CDS Market and its Determinants

This paper analyzes the network structure of the credit default swap (CDS) market, using a unique sample of counter-parties’ bilateral notional exposures to CDS on 642 sovereign and financial reference entities. We study the network structure, similarly to the literature on interbank and payment systems, by computing a variety of network metrics at the aggregated level and for several sub-networks. At a reference entity level, we analyze the determinants of some key network properties for large reference entities. Our main results, obtained on a sub-sample of 191 reference entities, are the following. First, the CDS network shows topological similarities with the interbank network, as we document a “small world” structure and a scale-free degree distribution for the CDS market. Second, there is considerable heterogeneity in the network structures across reference entities. In particular, the outstanding debt volume and its structure (maturity, collateralization), the riskiness, the type (sovereign/financial) and the location (European/non-European) of reference entities significantly influence the size, the activity and the concentration of the CDS exposure network. For instance, the network on a high-volatility reference entity is typically more active, larger in size and less concentrated.