Average Number Of Links Research Articles

Tortuosity of Delaunay Triangulations and Statistics of Shortest Paths

A tortuosity τ Dln of the Delaunay triangulation on plane and in 3D-space is defined and numerically calculated. This coefficient appears naturally in the porous media studies. The conjecture on the average number of links in the shortest path between two arbitrary points is formulated and statistically studied. The distribution of the number of links in the shortest paths in triangulations of square and disc on R 2 is described.

Arithmetic Study about Efficiency in Network Topologies for Data Centers

Data centers are getting more and more attention due the rapid increase of IoT deployments, which may result in the implementation of smaller facilities being closer to the end users as well as larger facilities up in the cloud. In this paper, an arithmetic study has been carried out in order to measure a coefficient related to both the average number of hops among nodes and the average number of links among devices for a range of typical network topologies fit for data centers. Such topologies are either tree-like or graph-like designs, where this coefficient provides a balance between performance and simplicity, resulting in lower values in the coefficient accounting for a better compromise between both factors in redundant architectures. The motivation of this contribution is to craft a coefficient that is easy to calculate by applying simple arithmetic operations. This coefficient can be seen as another tool to compare network topologies in data centers that could act as a tie-breaker so as to select a given design when other parameters offer contradictory results.

Biased-voter model: How persuasive a small group can be?

We study the voter model dynamics in the presence of confidence and bias. We assume two types of voters. Unbiased voters whose confidence is indifferent to the state of the voter and biased voters whose confidence is biased towards a common fixed preferred state. We study the problem analytically on the complete graph using mean field theory and on an Erdős-Rényi random network topology using the pair approximation, where we assume that the network of interactions topology is independent of the type of voters. We find that for the case of a random initial setup, and for sufficiently large number of voters N, the time to consensus increases proportionally to log(N)/γv, with γ the fraction of biased voters and v the parameter quantifying the bias of the voters (v = 0 no bias). We verify our analytical results through numerical simulations. We study this model on a topology of the network of interactions depending on the bias, and examine two distinct, global average-degree preserving strategies (model I and model II) to obtain such random topologies starting from the random topology independent of bias case as the initial setup. Keeping all other parameters constant, in model I, μBU, the average number of links among biased (B) and unbiased (U) voters is varied at the expense of μUU and μBB, i.e. the average number of links among only unbiased and biased voters respectively. In model II, μBU is kept constant, while μBB is varied at the expense of μUU. We find that if the agents follow the strategy described by model II, they can achieve a significant reduction in the time to reach consensus as well as an increment in the probability to reach consensus to the preferred state. Hence, persuasiveness of the biased group depends on how well its members are connected among each other, compared to how well the members of the unbiased group are connected among each other.

Pseudo-Darwinian evolution of physical flows in complex networks

The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and “Pseudo-Darwinian” strategy. At each evolution step and regarding the selected strategy, one removes either a randomly chosen link, or the link carrying the strongest flux, or the link with the weakest flux, respectively. We study how the network structure and the total flux between randomly chosen source and drain nodes evolve. We discover a universal power-law decrease of the total flux, followed by an abrupt transport collapse. The time of collapse is shown to be determined by the average number of links per node in the initial network, highlighting the importance of this network property for ensuring safe and robust transport against random failures, intentional attacks and maintenance cost optimizations.

Multiple urban stressors drive fish-based ecological networks in streams of Columbus, Ohio, USA

Integrating a network perspective into multiple-stressor research can reveal indirect stressor effects and simultaneously estimate both taxonomic and functional community characteristics, thus representing a novel approach to stressor paradigms in rivers. Using six years of data from twelve streams of Columbus, Ohio, USA, the effects of nutrients (N:P), impervious surface (%IS), and sedimentation on network properties were quantified. Variability in the strength and distribution of trophic interactions was assessed by incorporating biomass into networks. All stressors impacted some properties of network topology – linkage density (average number of links per species), connectance (fraction of all possible links realized in a network), and compartmentalization (degree to which networks contain discrete sub-webs), including synergistic interactive effects between sedimentation and stream size. We also found support for antagonistic effects between (1) sedimentation and %IS and between %IS and N:P on the weighted index mean link weight, which represents the magnitude of trophic interactions among species in a network, and (2) %IS and stream size on strength standard deviation, a measure of the distribution of total magnitude of all trophic interactions per species in a network. Overall, our results point to the potential for urban stressors such as impervious surfaces and sedimentation – alone and as interactions – to decrease network complexity, compartmentalization, and stability, likely through homogenizing habitat and limiting food resources. The observation that larger streams often buffered the negative effects of these stressors suggests that restoration and other management approaches might be most beneficial in smaller headwater streams of urban catchments.

The Architecture of the Network of Orchid–Fungus Interactions in Nine Co-occurring Dendrobium Species

Orchid-fungus interaction networks often consist of many different fungi that interact with co-occurring orchids in complex ways, but so far it remains largely unclear which processes determine network structure and both ecological and evolutionary mechanisms have been invoked to explain network architecture. In this research, we tested the hypothesis that closely related orchids associate with similar mycorrhizal fungi and vice versa by investigating the architecture of the interaction network between orchid mycorrhizal fungi (OMF) and nine co-occurring epiphytic Dendrobium species. All species grew on the bark of a single tree species (Camelia sinensis) in a traditional tea garden in China, which allowed us to assess the role of evolutionary history in determining the assembly of orchid-fungus communities without the confounding effects of environmental variation. In total, 101 different fungal operational taxonomic units (OTUs) known to be mycorrhizal in orchids were found. Most of the identified mycorrhizal OTUs were members of the Serendipitaceae (80% of all identified mycorrhizal sequences). All orchid species associated with a large number of fungi (average number of links: 31.6 ± 3.8), and orchids from the same species tended to have significantly more similar fungal partners than orchids from different species. The network of interactions was significantly nested (NODF = 41.59, p < 0.01), but not significantly compartmentalized (M = 0.26, Mrandom = 0.27). Phylogenetic analyses showed that the interaction network was not significantly affected by the phylogenies of the orchids or the fungi. Overall, these results indicate that the studied orchid species associated with multiple fungi simultaneously, and that the network of associations was built on asymmetric and weak reciprocal dependences. Associating with multiple fungi may be a successful strategy of orchids to colonize vacant sites and to increase survival of established plants in epiphytic habitats.

Bibliometric Trends in Quantum Information Processing

The results of a bibliometric analysis of studies on quantum information processing for 2000–2017 are presented. We used Science Citation Index Expanded (SCIE) as a data source. This article reveals countries with significant volumes of research, as well as the main participants in the “quantum race.” The structure of a coauthor network was studied in terms of the analysis of social networks using the Salton index; in the analysis of citation, indicators were used based on the calculation of not only the average number of links to a publication, but also highly cited publications in the top 1 and top 10%. The sources and structure of sponsorship of published results in the field of quantum information processing are identified. The positions of Russia are evaluated on all considered indicators.

Simulating social distancing measures in household and close contact transmission of SARS-CoV-2.

We sought to evaluate contact rate reduction goals for household and close contacts and to provide preventive recommendations during the coronavirus pandemic. We applied an agent-based model to simulate the transmission dynamics of SARS-CoV-2 within household or close contacts through a social network of 150 nodes. there is no great difference in total infected people within modifications in number of links per node for networks with average number of links per node greater than three. For six nodes, total infected people are 149.85; for five nodes, 148.97; and for four nodes, 141.57. On the other hand, for three nodes, total infected are 82.39, for two nodes, 13.95; and for one node, 2.96. This model indicates a possible pitfall if social distancing measures are not stepwise suspended and close surveillance of cases are not provided, since the relationship between average links per node and number of infected people seems to be s-shaped, and not linear.

Stochastic model of information - computer network blocking in generation and transmission of malicious big data

This work reviews a stochastic model of information -computer networks blocking in generation and transmission of large volumes of malicious data, developed by the authors. Rapid development of the Internet of things (IoT) leads to short time emergence of tens and hundreds of millions of new devices with their IP – addresses in the global network, capable to form a very large -scale botnets in case of infection. Therefore, development of network blocking models when generating and transmitting large amounts of malicious data is a crucial task to solve the problem of traffic filtering and balancing. When creating the model, we considered probability diagrams of transitions between possible states (share of infected devices) of computer networks, which describe the logic of the on-going processes. Based on approach used, the nonlinear second-order differential equation was deduced, allowing to formulate and solve boundary problems for determination of time-dependence of the probability density function for observation of different system states.The resulting differential equation contains the second and first time - derivatives, and the derivatives with respect to a variable, describing the change in the state of the system under consideration. Considering the second time - derivative of the probability density corresponds to the case in which the existing states generate additional new states, causing acceleration of processes and self-organization.The created model allows to assess time to achieve the state, when there is a limit value of share of potentially infected devices or, for example, achievement of its percolation threshold in a computer network. Percolation threshold is the minimum percentage of blocked nodes, at which the entire network loses the information transmission features (there is no free path between any randomly selected nodes). Using the approach adopted in the theory of percolation allowed to link structural and information characteristics of networks, such as dependence of their percolation threshold on the average number of links per node (network density) with dynamic characteristics of their blocking (time to reach the percolation threshold).

Vehicle-Mounted Base Station for Connected and Autonomous Vehicles: Opportunities and Challenges

The crown jewel of intelligent transportation is achieving autonomous driving that can ultimately become accident- and congestion-free through CAVs and the associated traffic management systems. Recently, this vision has sparked huge research interest, such as IoV, LTE-V2X, and 5G. However, the huge amount of traffic data generated by CAVs poses challenges for the current networks and even the upcoming 5G communication networks.In this article, we first analyze the communication requirements of CAVs and present the progress of vehicular communication networks, and on that basis propose the novel concept of VMBS and a VMBS-CCNA for CAVs. The VMBS plays multiple roles of a user node and edge computing node for external communication networks, and a base station and information caching node for CAVs, thus achieving the fusion of communication and computing for CAVs. To this end, we present both the VMBS-enabled wireless communication and computing for CAVs, and the VMBS-assisted wireless communication for other wireless devices. Several research challenges and some open research issues are highlighted and discussed. Finally, simulation results reveal that the proposed VMBS-CCNA can bring a significant improvement in terms of throughput, delay, and average number of links.

The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

Analyses of the processes of information transfer within network structures shows that the conductivity and percolation threshold of the network depend not only on its density (average number of links per node), but also on its spatial symmetry groups and topological dimension. The results presented in this paper regarding conductivity simulation in network structures show that, for regular and random 2D and 3D networks, an increase in the number of links (density) per node reduces their percolation threshold value. At the same network density, the percolation threshold value is less for 3D than for 2D networks, whatever their structure and symmetry may be. Regardless of the type of networks and their symmetry, transition from 2D to 3D structures engenders a change of percolation threshold by a value exp{−(d − 1)} that is invariant for transition between structures, for any kind of network (d being topological dimension). It is observed that in 2D or 3D networks, which can be mutually transformed by deformation without breaking and forming new links, symmetry of similarity is observed, and the networks have the same percolation threshold. The presence of symmetry axes and corresponding number of symmetry planes in which they lie affects the percolation threshold value. For transition between orders of symmetry axes, in the presence of the corresponding planes of symmetry, an invariant exists which contributes to the percolation threshold value. Inversion centers also influence the value of the percolation threshold. Moreover, the greater the number of pairs of elements of the structure which have inversion, the more they contribute to the fraction of the percolation threshold in the presence of such a center of symmetry. However, if the center of symmetry lies in the plane of mirror symmetry separating the layers of the 3D structure, the mutual presence of this group of symmetry elements do not affect the percolation threshold value. The scientific novelty of the obtained results is that for different network structures, it was shown that the percolation threshold for the blocking of nodes problem could be represented as an additive set of invariant values, that is, as an algebraic sum, the value of the members of which is stored in the transition from one structure to another. The invariant values are network density, topological dimension, and some of the elements of symmetry (axes of symmetry and the corresponding number of symmetry planes in which they lie, centers of inversion).

A Spammer Identification Method for Class Imbalanced Weibo Datasets

Nowadays, Weibo has become a significant and popular information sharing platform in China. Meanwhile, spammer identification has been a big challenge for it. To mitigate the damage caused by spammers, classification algorithms from machine learning have been applied to distinguish spammers and non-spammers. However, most of the previous studies overlook the class imbalance problem of real-world data. In this paper, by analyzing the characteristics of spammers in Weibo, we select microblog content similarity, the average number of links, and the other 12 features to construct a comprehensive feature vector never seen before. Considering the existence of imbalance problems in spammer identification, an ensemble learning method is used to combine multiple base classifiers for improving the learning performance. During the training stage of base learners, fuzzy-logic-based oversampling and cost-sensitive support vector machine are considered to tackle imbalanced data at both data and algorithmic levels. The experimental results demonstrate that compared with the existing state-of-the-art methods, the recall rate of our proposed approach increases by 6.5% and reaches the precision value of 87.53% when used to deal with real-world Weibo datasets we collected.

Bribery games on interdependent complex networks

Bribe demands present a social conflict scenario where decisions have wide-ranging economic and ethical consequences. Nevertheless, such incidents occur daily in many countries across the globe. Harassment bribery constitute a significant sub-set of such bribery incidents where a government official demands a bribe for providing a service to a citizen legally entitled to it. We employ an evolutionary game-theoretic framework to analyse the evolution of corrupt and honest strategies in structured populations characterized by an interdependent complex network. The effects of changing network topology, average number of links and asymmetry in size of the citizen and officer population on the proliferation of incidents of bribery are explored. A complex network topology is found to be beneficial for the dominance of corrupt strategies over a larger region of phase space when compared with the outcome for a regular network, for equal citizen and officer population sizes. However, the extent of the advantage depends critically on the network degree and topology. A different trend is observed when there is a difference between the citizen and officer population sizes. Under those circumstances, increasing randomness of the underlying citizen network can be beneficial to the fixation of honest officers up to a certain value of the network degree. Our analysis reveals how the interplay between network topology, connectivity and strategy update rules can affect population level outcomes in such asymmetric games.

Critical properties of the antiferromagnetic Ising model on rewired square lattices

The effect of randomness on critical behavior is a crucial subject in condensed matter physics due to the the presence of impurity in any real material. We presently probe the critical behaviour of the antiferromagnetic (AF) Ising model on rewired square lattices with random connectivity. An extra link is randomly added to each site of the square lattice to connect the site to one of its next-nearest neighbours, thus having different number of connections (links). Average number of links (ANOL) κ is fractional, varied from 2 to 3, where κ = 2 associated with the native square lattice. The rewired lattices possess abundance of triangular units in which spins are frustrated due to AF interaction. The system is studied by using Monte Carlo method with Replica Exchange algorithm. Some physical quantities of interests were calculated, such as the specific heat, the staggered magnetization and the spin glass order parameter (Edward-Anderson parameter). We investigate the role played by the randomness in affecting the exisiting phase transition and its interplay with frustration to possibly bring any spin glass (SG) properties. We observed the low temperature magnetic ordered phase (Néel phase) preserved up to certain value of κ and no indication of SG phase for any value of κ.

Quantifying noise in mass spectrometry and yeast two-hybrid protein interaction detection experiments.

Protein interaction networks (PINs) are popular means to visualize the proteome. However, PIN datasets are known to be noisy, incomplete and biased by the experimental protocols used to detect protein interactions. This paper aims at understanding the connection between true protein interactions and the protein interaction datasets that have been obtained using the most popular experimental techniques, i.e. mass spectronomy and yeast two-hybrid. We start from the observation that the adjacency matrix of a PIN, i.e. the binary matrix which defines, for every pair of proteins in the network, whether or not there is a link, has a special form, that we call separable. This induces precise relationships between the moments of the degree distribution (i.e. the average number of links that a protein in the network has, its variance, etc.) and the number of short loops (i.e. triangles, squares, etc.) along the links of the network. These relationships provide powerful tools to test the reliability of datasets and hint at the underlying biological mechanism with which proteins and complexes recruit each other.

Identifying missing relevant patent citation links by using bibliographic coupling in LED illuminating technology

This study uses bibliographic coupling to identify missing relevant patent links, in order to construct a comprehensive citation network. Missing citation links can be added by taking the missing relevant patent links into account. The Pareto principle is used to determine the threshold of bibliographic coupling strength, in order to identify the missing relevant patent links. Comparisons between the original patent citation network and the comprehensive patent citation network with the missing relevant patent links are illustrated at both the patent and assignee levels. Light emitting diode (LED) illuminating technology is chosen as the case study. The relationships between the patents and the assignees are obviously enhanced after adding the missing relevant patent links. The results show that the growth rates on both the total number and the average number of links have apparently improved at the patent level. At the assignee level, the number of linked assignees and the average number of links between two assignees are increased. The differences between the two citation networks are further examined by means of the Freeman vertex betweenness centrality and Johnson's hierarchical clustering. The patents with more new links to other patents have distinct results in terms of the Freeman vertex betweenness centrality. The enhancement of links among patents also results in different clustering.

Radiation telomerization of tetrafluoroethylene in butyl chloride solution

The kinetics of the radiation-initiated polymerization of tetrafluoroethylene (TFE) in butyl chloride has been studied. The rate of the process, the properties and yield of telomers obtained depend on the initial concentration of TFE (2.6–22 wt %) in the solution and the dose of γ-irradiation. The analysis of the measured IR absorption spectra and a possible scheme of the process allow to suggest that the main product of the reaction is C4H8Cl(C2F4)n−1CF2CF2H with the formation of small amounts of C4H9(C2F4)n−1CF2CF2H and Cl(C2F4)n−1CF2CF2H. The average number of links in the telomer (n) increases from 7.6 to 16.1 when the concentration of the monomer in the solution varies in the range of 7–22 wt %. The length of the chain of the soluble telomers (n) does not depend on the initial concentration of TFE and makes ∼7.

Sampling from scale-free networks and the matchmaking paradox

Consider a large finite scale-free network consisting of M>>1 nodes and N>>1 links, in which the degree distribution of links per bond is governed by a power-law P(n) approximately n(-1-alpha) with exponent 0<alpha<1. A subset of m<<M nodes is sampled arbitrarily, yielding the empirical sample mean eta : the average number of links per node, within the sampled subset. We explore the statistics of the sample mean eta and show that its fluctuations around the network mean nu=N/M are extremely broad and strongly skewed--yielding typical values, which are systematically and significantly smaller than the network mean nu. Applying these results to the case of bipartite scale-free networks, we show that the sample means of the two parts of these networks generally differ--a fact we refer to as the "matchmaking paradox."

On Game Theoretic Peer Selection for Resilient Peer-to-Peer Media Streaming

Peer-to-peer (P2P) media streaming quickly emerges as an important application over the Internet. A plethora of approaches have been suggested and implemented to support P2P media streaming. In our study, we first classified existing approaches and studied their characteristics by looking at three important quantities: number of upstream peers (parents), number of downstream peers (children), and average number of links per peer. In existing approaches, peers are assigned with a fixed number of parents without regard to their contributions, measured by the amount of outgoing bandwidths. Obviously, this is an undesirable arrangement as it leads to highly inefficient use of the P2P links. This observation motivates us to model the peer selection process as a cooperative game among peers. This results in a novel peer selection protocol such that the number of upstream peers of a peer is related to its outgoing bandwidth. Specifically, peers with larger outgoing bandwidth are given more parents, which make them less vulnerable to peer dynamics. Simulation results show that the proposed protocol improves delivery ratio using similar number of links per peer, comparing with existing approaches under a wide range of system parameters.

Stability of a model food web

We investigate numerically the stability of a model food web, introduced by Nunes Amaral and Meyer [Phys. Rev. Lett. 82, 652 (1999)]. The model describes a system of species located in niches at several levels. Upper level species are predating on those from a lower level. We show that the model web is more stable when it is larger, although the number of niches is more important than the number of levels. The food web is self-organizing itself, trying to reach a certain degree of complexity, i.e., number of species and links among them. If the system cannot achieve this state, it will go extinct. We demonstrate that the average number of links per species and the reduced number of species depend in the same way on the number of niches. We also determine how the stability of the food web depends on another parameter of the model, the killing probability. Despite keeping the ratio of the creation and killing probabilities constant, increasing the latter reduces significantly the stability of the model food web. We show that connectance dependence on the number of niches has a power-type character, which agrees with the field data, and that it decreases with the number of species also as a power-type function.