Vertices In Network Research Articles

On an extremal family of circulant networks

The paper addresses the optimization problem for circulant networks of maximizing the number of vertices given the degree and diameter of a graph. For the graphs in the best available extremal family of circulant networks, we improve the estimate for diameter, which together with previous results for multiplicative circulant networks enables us to improve the lower bounds for the attainable number of vertices of circulant networks of all dimensions k ≥ 4.

DETECTING CHAOS TIME SERIES VIA COMPLEX NETWORK FEATURE

In this paper, an effective method from time series to complex network via phase space reconstruction is introduced. We reconstruct the phase space from a time series by the time-delay coordinate method. Each state vector of phase space is regarded as a vertex of network and the connection is based on the distance of the vertices in phase space. The networks corresponding to various time series, the x component of the chaotic Rössler system, noisy periodic time series and random series, display different topology feature. So we can determine whether a time series is chaotic series by the topology feature of corresponding network. Finally, the daily stream-flow series of Yangtze River is investigated to validate the effective of our method.

Some problems in distributed computational geometry

In a planar geometric network vertices are located in the plane, and edges are straight line segments connecting pairs of vertices, such that no two of them intersect. In this paper we study distributed computing in asynchronous, failure-free planar geometric networks, where each vertex is associated to a processor, and each edge to a bidirectional message communication link. Processors are aware of their locations in the plane. We consider fundamental computational geometry problems from the distributed computing point of view, such as finding the convex hull of a geometric network and identification of the external face. We also study the classic distributed computing problem of leader election, to understand the impact that geometric information has on the message complexity of solving it. We obtain an O ( n log 2 n ) message complexity algorithm to find the convex hull, and an O ( n log n ) message complexity algorithm to identify the external face of a geometric network of n processors. We present a matching lower bound for the external face problem. We prove that the message complexity of leader election in a geometric ring is Ω ( n log n ) , hence geometric information does not help in reducing the message complexity of this problem.

Super connectivity of k-regular interconnection networks

Super connectivity is an important issue in interconnection networks. It has been shown that if a network possesses the super connectivity property, it has a high reliability and a small vertex failure rate. Many interconnection networks, like the hypercubes, twisted-cubes, crossed-cubes, möbius cubes, split-stars, and recursive circulant graphs, are proven to be super connected; and the augmented cubes are maximum connected. However, each network vertex has a higher degree as long as the number of vertices increases exponentially. For example, each vertex of the hypercube Q n has a degree of n, and each vertex of the augmented cube AQ n has a degree of 2 n − 1. In this paper, we not only show that the augmented cube AQ n is super connected for n = 1, 2 and n ⩾ 4, but also propose a variation of AQ n , denoted by AQ n, i , such that V( AQ n, i ) = V( AQ n ), E( AQ n, i ) ⊆ E( AQ n ), and AQ n, i is i-regular with n ⩾ 3 and 3 ⩽ i ⩽ 2 n − 1, in which AQ n, i is also super connected. In addition, we state the diameter of AQ n, i .

Approximate Inference Algorithm Based on Adaptive Ant Colony and Artificial Fish Swarm Algorithm for Credal Networks

This paper presents a new algorithm for approximate inference in credal networks (that is, models based on directed acyclic graphs and interval-valued probabilities). Approximate inference in credal networks can be considered as multistage decision in this paper. It is looked as combinatorial optimization problems that obtaining the extreme posteriors from the combinations of various vertices in credal networks. Based on this, the paper combines two intelligence swarm algorithms (ant colony algorithm and artificial fish swarm algorithm) to obtain interval posterior probabilities of query variable for the states of given evidence variables.

Network Topology for the Application Research of Electrical Control System Fault Propagation

Fault diagnosis and failure analysis is crucial issue in the process of health management and predicative maintenance for large complex system. Fault propagation and its cause-effect relationship in the system are of priority with regard to the fault diagnosis. The fundamentals for modeling the network topology are presented according to the characteristics of the electrical control system connection relationship and its functionality, a complex network topology model was built subsequently. The cause and effect relationships of the components are mapped to the relationships of the vertices in a complex network. The search method for the fault propagation path from the source vertex to the target vertex is studied using node coordinates connections, and application research of electrical control system fault propagation is shown and discussed in the paper. The proposed method is practical in dealing with the fault analysis and evaluation for large complex systems.

BrainNetVis: An Open-Access Tool to Effectively Quantify and Visualize Brain Networks

This paper presents BrainNetVis, a tool which serves brain network modelling and visualization, by providing both quantitative and qualitative network measures of brain interconnectivity. It emphasizes the needs that led to the creation of this tool by presenting similar works in the field and by describing how our tool contributes to the existing scenery. It also describes the methods used for the calculation of the graph metrics (global network metrics and vertex metrics), which carry the brain network information. To make the methods clear and understandable, we use an exemplar dataset throughout the paper, on which the calculations and the visualizations are performed. This dataset consists of an alcoholic and a control group of subjects.

Stronger Bounds on Braess's Paradox and the Maximum Latency of Selfish Routing

We give several new upper and lower bounds on the worst-case severity of Braess's paradox and the price of anarchy of selfish routing with respect to the maximum latency objective. In single-commodity networks with arbitrary continuous and nondecreasing latency functions, we prove that this worst-case price of anarchy is exactly $n-1$, where n is the number of network vertices. For Braess's paradox in such networks, we prove that removing at most c edges from a network decreases the common latency incurred by traffic at equilibrium by at most a factor of $c+1$. In particular, the worst-case severity of Braess's paradox with a single edge removal is maximized in Braess's original four-vertex network. In multicommodity networks, we exhibit an infinite family of two-commodity networks, related to the Fibonacci numbers, in which both the worst-case severity of Braess's paradox and the price of anarchy for the maximum latency objective grow exponentially with the network size. This construction demonstrates that numerous known selfish routing results for single-commodity networks have no analogues in networks with two or more commodities. We also prove an upper bound on both of these quantities that is exponential in the network size and independent of the network latency functions, showing that our construction is close to optimal. Finally, we use our family of two-commodity networks to exhibit a natural network design problem with intrinsically exponential (in)approximability.

Query Processing Using Distance Oracles for Spatial Networks

The popularity of location-based services and the need to do real-time processing on them has led to an interest in performing queries on transportation networks, such finding shortest paths and finding nearest neighbors. The challenge here is that the efficient execution of spatial operations usually involves the computation of distance along a spatial network instead of as the crow flies, which is not simple. Techniques are described that enable the determination of the network distance between any pair of points (i.e., vertices) with little O(n) space rather than having to store the n2 distances between all pairs. This is done by being willing to expend a bit more time to achieve this goal such O(log n) instead of O(1), well by accepting an error e in the accuracy of the distance that is provided. The strategy that is adopted reduces the space requirements and is based on the ability to identify groups of source and destination vertices for which the distance is approximately the same within some e. The reductions are achieved by introducing a construct termed a distance oracle that yields an estimate of the network distance (termed the e-approximate distance) between any two vertices in the spatial network. The distance oracle is obtained by showing how to adapt the well-separated pair technique from computational geometry to spatial networks. Initially, an e-approximate distance oracle of size O(n/(e2)) is used that is capable of retrieving the approximate network distance in O(log n) time using a B-tree. The retrieval time can be theoretically reduced further to O(1) time by proposing another e-approximate distance oracle of size O((n log n)/(e2)) that uses a hash table. Experimental results indicate that the proposed technique is scalable and can be applied to sufficiently large road networks. For example, a 10-percentapproximate oracle (e = 0.1) on a large network yielded an average error of 0.9 percent with 90 percent of the answers having an error of 2 percent or less and an average retrieval time of 68 μ seconds. The fact that the network distance can be approximated by one value is used to show how a number of spatial queries can be formulated using appropriate SQL constructs and a few built-in primitives. The result is that these operations can be executed on almost any modern database with no modifications, while taking advantage of the existing query optimizers and query processing strategies.

Which hole is leaking the most: a topological approach to study open systems

We study the process of escape of orbits through a hole in the phase space of a dynamical system generated by a chaotic map of an interval. If this hole is an element of Markov partition we are able to use the machinery of symbolic dynamics and estimate the probability of an orbit to escape at the instant of time n in terms of the topological pressure over corresponding symbolic dynamical systems. We obtain exact formulae allowing us to compare different holes according to their ability to support escaping flow of orbits. These results are applicable to the classification of vertices of dynamical networks in terms of the loads on nodes and edges of a network.

Dynamic analysis on the topological properties of the complex network of international oil prices

To analyze the dynamic of crude oil price data using homogenous partition of coarse graining process,OK WTI Spot Price FOB from January 1986 to November 2009 was transformed into symbolic sequences consisting of three characters (R,e,D). The vertices of the oil price fluctuation network were 5-symbol strings in the number of 102(i.e.102 fluctuation patterns in durations of 5 days) linked in the network's topology by time sequence. It contained integrated information about interconnections and interactions between fluctuation patterns of oil price in network topology. The dynamical statistics of the degree, degree distribution, clustering coefficient and the shortest path length were calculated. The results indicated that the degree of the oil price sequence fluctuation network and the accumulated degree distribution show a power-law distribution, so did the node degree and the rank. The degree of the former 32 nodes was larger, and most oil price fluctuation models had the character with the escalating trend. Some nodes of the oil price fluctuation network had stronger ability in between centrality, and 24.5 percent of the nodes took part in the 80.97 percent of Between Centrality function. The average path length was 2.285, and the paths with length 2—3 were 86.8 percent, which verified the complex characteristics of the oil price fluctuation in network topology. This paper had guiding significance in identifying the topological importance of the node model and understanding the inherent law and information of the oil price fluctuation.

Exploring hierarchical and overlapping modular structure in the yeast protein interaction network

BackgroundDeveloping effective strategies to reveal modular structures in protein interaction networks is crucial for better understanding of molecular mechanisms of underlying biological processes. In this paper, we propose a new density-based algorithm (ADHOC) for clustering vertices of a protein interaction network using a novel subgraph density measurement.ResultsBy statistically evaluating several independent criteria, we found that ADHOC could significantly improve the outcome as compared with five previously reported density-dependent methods. We further applied ADHOC to investigate the hierarchical and overlapping modular structure in the yeast PPI network. Our method could effectively detect both protein modules and the overlaps between them, and thus greatly promote the precise prediction of protein functions. Moreover, by further assaying the intermodule layer of the yeast PPI network, we classified hubs into two types, module hubs and inter-module hubs. Each type presents distinct characteristics both in network topology and biological functions, which could conduce to the better understanding of relationship between network architecture and biological implications.ConclusionsOur proposed algorithm based on the novel subgraph density measurement makes it possible to more precisely detect hierarchical and overlapping modular structures in protein interaction networks. In addition, our method also shows a strong robustness against the noise in network, which is quite critical for analyzing such a high noise network.

The very small world of the well-connected

Online networks occupy an increasingly larger position in how we acquire information, how we communicate with one another, and how we disseminate information. Frequently, small sets of vertices dominate various graph and statistical properties of these networks and, because of this, they are relevant for structural analysis and efficient algorithms and engineering. For the web overall, and specifically for social linking in blogs and instant messaging, we provide a principled, rigorous study of the properties, the construction, and the utilization of subsets of special vertices in large online networks. We show that graph synopses defined by the importance of vertices provide small, relatively accurate portraits, independent of the importance measure, of the larger underlying graphs and of the important vertices. Furthermore, they can be computed relatively efficiently.

Grain Growth Simulations Including Particle Pinning Using the Multiphase-field Concept

In this paper, the effect of particle pinning on grain boundary motion is investigated by phase-field modeling. In general, the kinetics of grain growth in multicrystalline materials is determined by the interplay of curvature driven grain boundary motion and the balance of interfacial tension at the vertices of a grain boundary network. A comprehensive way to treat both effects in one model is given by the phase-field approach. The specific feature of the multiphase-field model used for this investigation is its ability to treat each grain or phase boundary with its individual characteristics, together with a thermodynamic coupling which allows a sound treatment of phase transformation, e.g. the formation of precipitates of a second phase.The pinning effect itself is simulated on the nanometer scale resolving the interaction of individual inert or reactive precipitates with a curved grain boundary. From these simulations an effective pinning force is deduced, and a model for a driving force dependent grain boundary mobility is formulated accounting for the pinning effect in the grain growth simulation on the mesoscopic scale. These simulations demonstrate how particle pinning leads to much slower growth kinetics and a different grain morphology with higher boundary curvatures in the stationary state. Finally, an increase of the pinning force due to a changing particle density, e.g. during heat treatment, is shown to result in a transition between normal and abnormal grain growth before grain coarsening is inhibited completely.

PHASE TRANSITION IN THE ISING MODEL ON LOCAL-WORLD EVOLVING NETWORKS

We study the critical behavior of the Ising model on the local-world evolving network. Monte Carlo simulations with the standard Metropolis local update algorithms are performed extensively on the network with different parameters. Ising spins put onto network vertices exhibit an effective phase transition from ferromagnetism to paramagnetism upon heating. The critical temperature has been demonstrated to increase linearly with the average degree of the network as TC ~ 〈k〉. Simulation results on local-world evolving networks with various parameters show logarithmical relationships of the critical temperature with the size of the local world as TC ~ ln (ml), and with the size of the network as TC ~ ln (N), respectively. The latter is the generalization of the conclusion for the Ising model on the Barabási–Albert scale-free network, a limiting case of the local-world evolving network.

Ranking Vertices or Edges of a Network by Loops: A New Approach

We introduce loop ranking, a new ranking measure based on the detection of closed paths, which can be computed in an efficient way. We analyze it with respect to several ranking measures which have been proposed in the past, and are widely used to capture the relative importance of the vertices in complex networks. We argue that loop ranking is a very appropriate measure to quantify the role of both vertices and edges in the network traffic.

The backup 2‐center and backup 2‐median problems on trees

AbstractIn this paper, we are concerned with the problem of deploying two servers in a tree network, where each server may fail with a given probability. Once a server fails, the other server will take full responsibility for the services. Here, we assume that the servers do not fail simultaneously. In the backup 2‐center problem, we want to deploy two servers at the vertices such that the expected distance from a farthest vertex to the closest functioning server is minimum. In the backup 2‐median problem, we want to deploy two servers at the vertices such that the expected sum of distances from all vertices to the set of functioning servers is minimum. We propose an O(n)‐time algorithm for the backup 2‐center problem and an O(n log n)‐time algorithm for the backup 2‐median problem, where n is the number of vertices in the given tree network. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009

Pinning control of directed dynamical networks based on ControlRank

By applying local feedback injections to a small fraction of network vertices, a dynamical network can be stabilized on a homogeneous equilibrium. However, different pinning strategies may lead to different performances. This paper develops a novel pinning scheme based on ControlRank (CR), which is a vertex centrality index exploring the link structure of the directed networks. Simulation study is given on a scale-free directed dynamical network, which demonstrates that it is much more effective to pin the vertex with largest CR than pin the vertex with largest out-degree.

Teasing out the missing links

Focusing on the hierarchical structure inherent in social and biological networks might provide a smart way to find missing connections that are not revealed in the raw data — which could be useful in a range of contexts. Networks are now a ubiquitous tool for representing the structure of complex systems, including the Internet, social networks, food webs, and protein and genetic networks. Unfortunately, the data describing these networks are in many cases incomplete or biased. A new study provides a general technique to divide network vertices into groups and sub-groups. Revealing such underlying hierarchies makes it possible to predict missing links from partial data with higher accuracy than previous methods.

An approach to research the topology of Chinese temperature sequence based on complex network

To analyze the dynamics of the temperature data, using homogenous partition of coarse graining process, the series of Chinese daily main temperature from 1961 to 2002 is transformed into symbolic sequences consisting of 5 characters {R,r,e,d,D}. The vertices of the temperature fluctuation network is 125 3-symbol strings (i.e., 125 fluctuation patterns in durations of 4 days), linked in the network's topology by time sequence. It contains Integrated information about interconnections and interactions between fluctuation patterns of temperature in network topology. Random fluctuant network and chaos fluctuant network by using random sequence and chaos sequence of Lorenz system were built. We calculated the dynamical statistics of the degrees and the distribution of degrees, clustering coefficient and the shortest path length, and compared the difference of these three sequences from the view point of network. The result is that. The main vertices of temperature fluctuant network generally contain the 3 characters R, r and e, and corresponding the background of global warming, the feature of temperature fluctuation is mainly ascending. On all accounts, the temperature fluctuant network is similar with chaos network in its dynamical statistics, but is markedly different from random network, which reflects the complexity of temperature fluctuation. And besides, some vertices in temperature fluctuant network have high betweenness centrality (BC), 4% of vertices bear 71.9% of betweenness centrality of networks, these vertices of importance in topological statistics are helpful to understanding the inherent law and information transmission. The vertices' BC in chaos network is similar with that of the temperature network, but vertices in random network almost have identical betweenness centrality. As a result, the patterns of temperature fluctuation corresponding to the process of weather change have similar property with chaos rather than the random fluctuation process.