Average Shortest Path Length Research Articles

A network theoretic study of ecological connectivity in Western Himalayas

Network theoretic approach has been used to model and study the flow of ecological information, growth and connectivity on landscape level of anemochory (wind dispersal) of Himalayan moist temperate forest species in the Western Himalaya region. A network is formally defined and derived for seed dispersion model of target floral species where vertices represent habitat patches which are connected by an edge if the distance between the patches is less than a threshold distance. We define centrality of a network and computationally identify the habitat patches that are central to the process of seed dispersion to occur across the network. These central patches are located on map and geographical regions critically important for the flow of ecological information across the network are identified as Gharwal region and eastern Himachal Pradesh of Indian Himalaya. We find that the network of habitat patches is a scale-free network and at the same time it also displays small-world property characterized by high clustering and low average shortest path length. As a result, ecological information propagates rapidly and evenly on a local scale. Hubs in the network are identified as important centres for dissemination of ecological information (seeds) and need to be conserved against a potential attack by malicious agents and also ecological shocks. The network showcase a well-formed community structure. As a consequence of these structural properties of the network, anemochory floral species studied in this work are likely to thrive across the ecological network of forest patches in the Western Himalaya region over time.

Comparative study on the topological structure of China Education Network

China Education Network (CEN) of year 2014 was studied as a complex network object. By searching the domain of “.edu.cn” and filtering some unexpected results, we finally get a network with 14,100,628 pages and 213,513,401 links. The topology of this network was studied to get the features such as out-degree distribution, in-degree distribution and average shortest path length. These features were compared with that of year 2007 and 2004 to observe the evolution mechanisms of CEN. According to the statistical results, it is found that some topology features of CEN such as out-degree distribution, in-degree distribution and average shortest path have changed a lot and the related reasons for these changes are given in this paper.

Proactive defense mechanisms for the software-defined Internet of Things with non-patchable vulnerabilities

The Internet of Things (IoT) contains a large number of heterogeneous devices with a variety of vulnerabilities. As the vulnerabilities can be exploited by the attackers to break into the system, it is of vital importance to patch all vulnerabilities. However, some vulnerabilities are impossible to patch (e.g., forever-day vulnerabilities). In order to deal with non-patchable vulnerabilities, we propose to change the attack surface of the IoT network to increase the attack effort. With the support of software-defined networking (SDN), we develop two proactive defense mechanisms that reconfigure the IoT network topology. We analyze how the security and performance change when the proposed solutions are deployed by using a graphical security model and various metrics in simulations. The results show our proactive defense mechanisms in the SD-IoT effectively increase the attack effort, while maintaining the average shortest path length.

Wavelet Multiresolution Complex Network for Analyzing Multivariate Nonlinear Time Series

Characterizing complicated behavior from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. We in this paper propose a novel wavelet multiresolution complex network (WMCN) for analyzing multivariate nonlinear time series. In particular, we first employ wavelet multiresolution decomposition to obtain the wavelet coefficients series at different resolutions for each time series. We then infer the complex network by regarding each time series as a node and determining the connections in terms of the distance among the feature vectors extracted from wavelet coefficients series. We apply our method to analyze the multivariate nonlinear time series from our oil–water two-phase flow experiment. We construct various wavelet multiresolution complex networks and use the weighted average clustering coefficient and the weighted average shortest path length to characterize the nonlinear dynamical behavior underlying the derived networks. In addition, we calculate the permutation entropy to support the findings from our network analysis. Our results suggest that our method allows characterizing the nonlinear flow behavior underlying the transitions of oil–water flows.

Financial networks based on Granger causality: A case study

Connectivity analysis is performed on a long financial record of 21 international stock indices employing a linear and a nonlinear causality measure, the conditional Granger causality index (CGCI) and the partial mutual information on mixed embedding (PMIME), respectively. Both measures aim to specify the direction of the interrelationships among the international stock indexes and portray the links of the resulting networks, by the presence of direct couplings between variables exploiting all available information. However, their differences are assessed due to the presence of nonlinearity. The weighted networks formed with respect to the causality measures are transformed to binary ones using a significance test. The financial networks are formed on sliding windows in order to examine the network characteristics and trace changes in the connectivity structure. Subsequently, two statistical network quantities are calculated; the average degree and the average shortest path length. The empirical findings reveal interesting time-varying properties of the constructed network, which are clearly dependent on the nature of the financial cycle.

Temporal slice registration and robust diffusion-tensor reconstruction for improved fetal brain structural connectivity analysis

Diffusion weighted magnetic resonance imaging, or DWI, is one of the most promising tools for the analysis of neural microstructure and the structural connectome of the human brain. The application of DWI to map early development of the human connectome in-utero, however, is challenged by intermittent fetal and maternal motion that disrupts the spatial correspondence of data acquired in the relatively long DWI acquisitions. Fetuses move continuously during DWI scans. Reliable and accurate analysis of the fetal brain structural connectome requires careful compensation of motion effects and robust reconstruction to avoid introducing bias based on the degree of fetal motion. In this paper we introduce a novel robust algorithm to reconstruct in-vivo diffusion-tensor MRI (DTI) of the moving fetal brain and show its effect on structural connectivity analysis. The proposed algorithm involves multiple steps of image registration incorporating a dynamic registration-based motion tracking algorithm to restore the spatial correspondence of DWI data at the slice level and reconstruct DTI of the fetal brain in the standard (atlas) coordinate space. A weighted linear least squares approach is adapted to remove the effect of intra-slice motion and reconstruct DTI from motion-corrected data. The proposed algorithm was tested on data obtained from 21 healthy fetuses scanned in-utero at 22–38 weeks gestation. Significantly higher fractional anisotropy values in fiber-rich regions, and the analysis of whole-brain tractography and group structural connectivity, showed the efficacy of the proposed method compared to the analyses based on original data and previously proposed methods. The results of this study show that slice-level motion correction and robust reconstruction is necessary for reliable in-vivo structural connectivity analysis of the fetal brain. Connectivity analysis based on graph theoretic measures show high degree of modularity and clustering, and short average characteristic path lengths indicative of small-worldness property of the fetal brain network. These findings comply with previous findings in newborns and a recent study on fetuses. The proposed algorithm can provide valuable information from DWI of the fetal brain not available in the assessment of the original 2D slices and may be used to more reliably study the developing fetal brain connectome.

Distributed Shortcut Networks: Low-Latency Low-Degree Non-Random Topologies Targeting the Diameter and Cable Length Trade-Off

Low communication latency becomes a main concern in highly parallel computers and supercomputers that reach millions of processing cores. Random network topologies are better suited to achieve low average shortest path length and low diameter in terms of the hop counts between nodes. However, random topologies lead to two problems: (1) increased aggregate cable length on a machine room floor that would become dominant for communication latency in next-generation custom supercomputers, and (2) high routing complexity that typically requires a routing table at each node (e.g., topology-agnostic deadlock-free routing). In this context, we first propose low-degree non-random topologies that exploit the small-world effect, which has been well modeled by some random network models. Our main idea is to carefully design a set of various-length shortcuts that keep the diameter small while maintaining a short cable length for economical passive electric cables. We also propose custom routing that uses the regularity of the various-length shortcuts. Our experimental graph analyses show that our proposed topology has low diameter and low average shortest path length, which are considerably better than those of the counterpart 3-D torus and are near to those of a random topology with the same average degree. The proposed topology has average cable length drastically shorter than that of the counterpart random topology, which leads to low cost of interconnection networks. Our custom routing takes non-minimal paths to provide lower zero-load latency than the minimal custom routings on different counterpart topologies. Our discrete-event simulation results using SimGrid show that our proposed topology is suitable for applications that have irregular communication patterns or non-nearest neighbor collective communication patterns.

Evolution of domestic airport networks: a review and comparative analysis

ABSTRACTPrevious studies on airport networks are strongly bounded time-wise or only conducted for single networks at distinct levels of abstraction and for distinct topological features. Here, we review and compare the evolution of domestic airport networks (DANs) for Australia, Brazil, Canada, China, India, Russia, US and Europe during the period 2002–2013. This is the first study on a consistent global dataset and allows for direct comparisons of network features. The air passenger traffic is tremendously increasing in all eight networks, with the largest number of passengers in US, followed by Europe and China. Degree distributions can often be best fitted with a truncated power-law (e.g. Brazil and US) or log-normal (e.g. Australia and Canada). While all eight networks clearly exhibit small-world properties, the average shortest path length is between 2.1 (China/Russia) and 4.0 (Canada). Our study sets a baseline for understanding the topology and evolution of DANs.

Network-based landscape of research strengths of universities in Mainland China

A landscape of a complex system presents a quantitative measure of its global state. The profile of research strength in Mainland China is investigated in detail, by which we illustrate a complex network based framework to extract a landscape from detailed records. First, a measure analogous to the Jaccard similarity is proposed to calculate from the presided funds similarities between the top-ranked universities. The neighbor threshold method is employed to reconstruct the similarity network of the universities. Second, the network is divided into communities. In each community the node with the largest degree and the smallest average shortest path length is taken as the representative of the community, called central node. The node bridging each pair of communities is defined to be a boundary. The central nodes and boundaries cooperatively give us a picture of the research strength landscape. Third, the evolutionary behavior is monitored by the fission and fusion probability matrices, elements of which are the percentage of a community at present time that joins into every community at the next time, and the percentage of a community at next time that comes from every present community, respectively. The landscapes in three successive 4-year durations are identified. It was found that some types of universities, such as the medicine&pharmacy and the finance&economy, conserve in single communities in the more than ten years, respectively. The agriculture&forest universities tend to cluster into one community. Meanwhile the engineering type distributes in different communities and tends to mix with the comprehension type. This framework can be used straightforwardly to analyze temporal networks. It provides also a new network-based method for multivariate time series analysis.

Statistical metrics for the characterization of karst network geometry and topology

Statistical metrics can be used to analyse the morphology of natural or simulated karst systems; they allow describing, comparing, and quantifying their geometry and topology. In this paper, we present and discuss a set of such metrics. We study their properties and their usefulness based on a set of more than 30 karstic networks mapped by speleologists. The data set includes some of the largest explored cave systems in the world and represents a broad range of geological and speleogenetic conditions allowing us to test the proposed metrics, their variability, and their usefulness for the discrimination of different morphologies.All the proposed metrics require that the topographical survey of the caves are first converted to graphs consisting of vertices and edges. This data preprocessing includes several quality check operations and some corrections to ensure that the karst is represented as accurately as possible. The statistical parameters relating to the geometry of the system are then directly computed on the graphs, while the topological parameters are computed on a reduced version of the network focusing only on its structure.Among the tested metrics, we include some that were previously proposed such as tortuosity or the Howard's coefficients. We also investigate the possibility to use new metrics derived from graph theory. In total, 21 metrics are introduced, discussed in detail, and compared on the basis of our data set. This work shows that orientation analysis and, in particular, the entropy of the orientation data can help to detect the existence of inception features. The statistics on branch length are useful to describe the extension of the conduits within the network. Rather surprisingly, the tortuosity does not vary very significantly. It could be heavily influenced by the survey methodology. The degree of interconnectivity of the network, related to the presence of maze patterns, can be measured using different metrics such as the Howard's parameters, global cyclic coefficient, or the average vertex degree. The average vertex degree of the reduced graph proved to be the most useful as it is simple to compute, it discriminates properly the interconnected systems (mazes) from the acyclic ones (tree-like structures), and it permits us to classify the acyclic systems as a function of the total number of branches. This topological information is completed by three parameters, allowing us to refine the description. The correlation of vertex degree is rather simple to obtain. It is systematically positive on all studied data sets indicating a predominance of assortative networks among karst systems. The average shortest path length is related to the transport efficiency. It is shown to be mainly correlated to the size of the network. Finally, central point dominance allows us to identify the presence of a centralized organization.

Multifractality and Network Analysis of Phase Transition.

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems.

How semantic memory structure and intelligence contribute to creative thought: a network science approach

ABSTRACTThe associative theory of creativity states that creativity is associated with differences in the structure of semantic memory, whereas the executive theory of creativity emphasises the role of top-down control for creative thought. For a powerful test of these accounts, individual semantic memory structure was modelled with a novel method based on semantic relatedness judgements and different criteria for network filtering were compared. The executive account was supported by a correlation between creative ability and broad retrieval ability. The associative account was independently supported, when network filtering was based on a relatedness threshold, but not when it was based on a fixed edge number or on the analysis of weighted networks. In the former case, creative ability was associated with shorter average path lengths and higher clustering of the network, suggesting that the semantic networks of creative people show higher small-worldness.

Evolution of the Mesoscopic Parameters and Mechanical Properties of Granular Materials upon Loading

Biaxial tests of granular materials under different lateral pressures were numerically simulated to study both the macromechanical behavior and evolution of mesoscopic parameters, including the coordination number, degree, clustering coefficient, and average shortest path length, which can provide information bridging mesoscale to macroscale of the mechanical properties of granular materials in a different and new way. The analysis results demonstrate that, with the increasing lateral pressure, there is a higher coordination number for denser granular material, and the coordination number of the samples eventually tends to the similar value at critical state with the same lateral pressure for different initial porosities; the distribution of the degree is very similar for samples with different initial porosities at critical state; the evolution of the clustering coefficients with axial strain is almost the same as that of the coordination number. At critical state, the clustering coefficients of all samples are almost identical, which means that the internal structures of samples with various initial porosities are similar; the average shortest path decreases with increasing lateral pressure and tends to be stable in the critical state. Additionally, the diameter of the contact network of granular material hardly changes at different lateral pressures at critical state.

Scalable and adaptive overlay for efficient forwarding in volunteer clouds

Volunteer cloud is a new concept of cloud computing where volunteers, i.e., user machines are used instead of or in addition to dedicated resources. Although volunteer clouds offer potential benefits in terms of energy and cost saving as well as elasticity, the volatility and the scalability of the volunteer resources are still open challenges that need to be investigated. In this paper, we focus on managing the connectivity in a scalable and dynamic fashion in volunteer clouds. We show that volunteer clouds could be modelled by a hierarchical small-world structure, characterised by short average path lengths among nodes, and strong local clustering, which implies small latency between nodes and therefore robust forwarding. Furthermore, we explore the benefits of the use of the recursive internetwork architecture (RINA) as a networking solution. Finally, simulation results show that our proposal achieves a trade-off between bounding the routing table size and ensuring transmission efficiency.

Scalable and adaptive overlay for efficient forwarding in volunteer clouds

Volunteer cloud is a new concept of cloud computing where volunteers, i.e., user machines are used instead of or in addition to dedicated resources. Although volunteer clouds offer potential benefits in terms of energy and cost saving as well as elasticity, the volatility and the scalability of the volunteer resources are still open challenges that need to be investigated. In this paper, we focus on managing the connectivity in a scalable and dynamic fashion in volunteer clouds. We show that volunteer clouds could be modelled by a hierarchical small-world structure, characterised by short average path lengths among nodes, and strong local clustering, which implies small latency between nodes and therefore robust forwarding. Furthermore, we explore the benefits of the use of the recursive internetwork architecture (RINA) as a networking solution. Finally, simulation results show that our proposal achieves a trade-off between bounding the routing table size and ensuring transmission efficiency.

Is the average shortest path length of gene set a reflection of their biological relatedness?

When a set of genes are identified to be related to a disease, say through gene expression analysis, it is common to examine the average distance among their protein products in the human interactome as a measure of biological relatedness of these genes. The reasoning for this is that, genes associated with a disease would tend to be functionally related, and that functionally related genes would be closely connected to each other in the interactome. Typically, average shortest path length (ASPL) of disease genes (although referred to as genes in the context of disease-associations, the interactions are among protein-products of these genes) is compared to ASPL of randomly selected genes or to ASPL in a randomly permuted network. We examined whether the ASPL of a set of genes is indeed a good measure of biological relatedness or whether it is simply a characteristic of the degree distribution of those genes. We examined the ASPL of genes sets of some disease and pathway associations and compared them to ASPL of three types of randomly selected control sets: uniform selection, from entire proteome, degree-matched selection, and random permutation of the network. We found that disease associated genes and their degree-matched random genes have comparable ASPL. In other words, ASPL is a characteristic of the degree of the genes and the network topology, and not that of functional coherence.

Coevolution of Cooperation and Partner Rewiring Range in Spatial Social Networks.

In recent years, there has been growing interest in the study of coevolutionary games on networks. Despite much progress, little attention has been paid to spatially embedded networks, where the underlying geographic distance, rather than the graph distance, is an important and relevant aspect of the partner rewiring process. It thus remains largely unclear how individual partner rewiring range preference, local vs. global, emerges and affects cooperation. Here we explicitly address this issue using a coevolutionary model of cooperation and partner rewiring range preference in spatially embedded social networks. In contrast to local rewiring, global rewiring has no distance restriction but incurs a one-time cost upon establishing any long range link. We find that under a wide range of model parameters, global partner switching preference can coevolve with cooperation. Moreover, the resulting partner network is highly degree-heterogeneous with small average shortest path length while maintaining high clustering, thereby possessing small-world properties. We also discover an optimum availability of reputation information for the emergence of global cooperators, who form distant partnerships at a cost to themselves. From the coevolutionary perspective, our work may help explain the ubiquity of small-world topologies arising alongside cooperation in the real world.

Longitudinal changes in functional connectivity of cortico-basal ganglia networks in manifests and premanifest huntington's disease.

Huntington's disease (HD) is a genetic neurological disorder resulting in cognitive and motor impairments. We evaluated the longitudinal changes of functional connectivity in sensorimotor, associative and limbic cortico-basal ganglia networks. We acquired structural MRI and resting-state fMRI in three visits one year apart, in 18 adult HD patients, 24 asymptomatic mutation carriers (preHD) and 18 gender- and age-matched healthy volunteers from the TRACK-HD study. We inferred topological changes in functional connectivity between 182 regions within cortico-basal ganglia networks using graph theory measures. We found significant differences for global graph theory measures in HD but not in preHD. The average shortest path length (L) decreased, which indicated a change toward the random network topology. HD patients also demonstrated increases in degree k, reduced betweeness centrality bc and reduced clustering C. Changes predominated in the sensorimotor network for bc and C and were observed in all circuits for k. Hubs were reduced in preHD and no longer detectable in HD in the sensorimotor and associative networks. Changes in graph theory metrics (L, k, C and bc) correlated with four clinical and cognitive measures (symbol digit modalities test, Stroop, Burden and UHDRS). There were no changes in graph theory metrics across sessions, which suggests that these measures are not reliable biomarkers of longitudinal changes in HD. preHD is characterized by progressive decreasing hub organization, and these changes aggravate in HD patients with changes in local metrics. HD is characterized by progressive changes in global network interconnectivity, whose network topology becomes more random over time. Hum Brain Mapp 37:4112-4128, 2016. © 2016 Wiley Periodicals, Inc.

Fast approximation of average shortest path length of directed BA networks

Abstract The average shortest path length is an important feature for complex networks. However, for large networks, it is very difficult to compute it due to the limitation of computing power. By analyzing the node reachability from several real BA networks as the example, we brought forward the concept of Global Reachable Nodes and Local Reachable Nodes. We found that the average shortest path length of a BA network is determined by the Global Reachable Nodes. From the mechanism of the BA network we illustrated this feature and hereby presented a randomized approximation algorithm for computing the average shortest path length. We verified the accuracy of this algorithm using 8 different networks. For large-scale BA network with millions of nodes, the experiments indicate that our method can estimate its ASPL with high accuracy using only several hundreds of Global Reachable Nodes.

A Comparison of Network-Based Metrics of Behavioral Degradation in Complex Engineered Systems

It has been assumed, but not yet tested, that the topological disintegration of networks is relatable to degradations in complex engineered system behavior and that extant network metrics are capable of capturing these degradations. This paper tests three commonly used network metrics used to quantify the topological robustness of networks for their ability to characterize the degree of failure in engineered systems: average shortest path length, network diameter, and a robustness coefficient. A behavioral network of a complex engineered system is subjected to “attack” to simulate potential failures to the system. Average shortest path length and the robustness coefficient showed topological disintegration patterns which differed between nominal and failed cases, regardless of failure implementation location. The network diameter metric is not sufficiently dependent on local cluster topology to show changes in topology with edge removal failure strategies. The results show that topological metrics from the field of complex networks are applicable to complex engineered systems when they account for both local and global topological changes.