High Clustering Coefficient Research Articles

Structural and spectral properties of the generalized corona networks

In this paper, we present a growing complex network model, namely, the generalized corona network (GCN) which is built on a base network and a sequence of networks by using corona product of graphs. This construction generalizes several existing complex network models. We study the structural properties of the special classes of generalized corona networks and show that these networks have small diameter, the cumulative betweenness distribution follows a power-law distribution, the degree distribution decay exponentially, small average path length with the network order, high clustering coefficient and small-world behavior. Further, we obtain the spectra of the adjacency matrix and the signless Laplacian matrix of GCN when the constituting networks are regular. Also, we obtain the Laplacian spectra for all generalized corona networks. In addition, explicitly give eigenvector corresponding to the adjacency and Laplacian eigenvalues. Finally, we derive the spectral radius and the algebraic connectivity of GCN.

Noise suppression ability and its mechanism analysis of scale-free spiking neural network under white Gaussian noise.

With the continuous improvement of automation and informatization, the electromagnetic environment has become increasingly complex. Traditional protection methods for electronic systems are facing with serious challenges. Biological nervous system has the self-adaptive advantages under the regulation of the nervous system. It is necessary to explore a new thought on electromagnetic protection by drawing from the self-adaptive advantage of the biological nervous system. In this study, the scale-free spiking neural network (SFSNN) is constructed, in which the Izhikevich neuron model is employed as a node, and the synaptic plasticity model including excitatory and inhibitory synapses is employed as an edge. Under white Gaussian noise, the noise suppression abilities of the SFSNNs with the high average clustering coefficient (ACC) and the SFSNNs with the low ACC are studied comparatively. The noise suppression mechanism of the SFSNN is explored. The experiment results demonstrate that the following. (1) The SFSNN has a certain degree of noise suppression ability, and the SFSNNs with the high ACC have higher noise suppression performance than the SFSNNs with the low ACC. (2) The neural information processing of the SFSNN is the linkage effect of dynamic changes in neuron firing, synaptic weight and topological characteristics. (3) The synaptic plasticity is the intrinsic factor of the noise suppression ability of the SFSNN.

Complex network dynamics of the topological structure in a geochemical field from the Nanling area in South China

The topological classification of geochemical elements is widely used as a reference for regional prospecting prediction. In this study, we analyze the topological correlation structures of 39 representative geochemical elements from the Nanling area of South China by implementing the complex networks theory. The topological correlation structures of geochemical elements have a high clustering coefficient (0.8120–0.8880), but the magnitude of the shortest path (1.2950–2.3600) is small. In combination with the analysis of complex networks characteristics, we report that the topological correlation structures of the geochemical elements in this area have small-world characteristics, which reveals the self-organized criticality. As shown in the topological network, two random elements have some level of associations, which present a specific community feature. Our preliminary result shows that with changing the control parameter (k) of “coarse-graining”, the topological correlation structures undergo two critical phase transitions. As the control parameter (k) reaches 0.44, the entire element system evolves into two parts. When the control parameter (k) reaches 0.63, the system forms three “communities”. It is worth noting that the three “communities” are basically consistent with the Goldschmidt’s geochemical classification of the elements, which are lithophile, siderophile, and chalcophile groups, respectively. In these “communities”, we also found that a small level of component units is nested.

Random growth networks with exponential degree distribution.

A great variety of complex networks can be well represented as random graphs with some constraints: for instance, a provided degree distribution, a smaller diameter, and a higher clustering coefficient. Among them, the degree distribution has attracted considerable attention from various science communities in the last few decades. In this paper, we focus mainly on a family of random graphs modeling complex networks that have an exponential degree distribution; i.e., P(k)∼ exp(αk), where k is the degree of a vertex, P(k) is a probability for choosing randomly a vertex with degree equal to k, and α is a constant. To do so, we first introduce two types of operations: type-A operation and type-B operation. By both the helpful operations, we propose an available algorithm A for a seminal model to construct exactly solvable random graphs, which are able to be extended to a graph space S(p,pc,t) with probability parameters p and pc satisfying p+pc=1. Based on the graph space S(p,pc,t), we discuss several topological structure properties of interest on each member N(p,pc,t) itself and find model N(p,pc,t) to exhibit the small-world property and assortative mixing. In addition, we also report a fact that in some cases, two arbitrarily chosen members might have completely different other topological properties, such as the total number of spanning trees, although they share a degree distribution in common. Extensive experimental simulations are in strong agreement with our analytical results.

Collaboration Relations in Climate Information Production and Dissemination to Subsistence Farmers in Namibia

Although climate information can aid farmers’ capacity to adapt to climate change, its accessibility and adoption by subsistence farmers hinge on the collaboration between farmers and climate information providers. This paper examines collaborations among actors in the process of climate information production and dissemination in the Namibian agricultural sector. The aim is to investigate the extent to which subsistence farmers are integrated into the collaboration process and the impact of the collaboration on the nature and accessibility of disseminated information. Key informant interviews and a questionnaire survey were used for data collection. Using network analysis, we estimated the networks’ density, clustering coefficient, and degree centrality. The study found that both the climate information production and dissemination networks have a high overall clustering coefficient (78% and 77%, respectively) suggesting a high rate of collaboration among the actors in the networks. However, the frequency of interactions between the actors in both the information production and dissemination networks and subsistence farmers remains very low. Nearly all surveyed farmers reported that they meet with information providers only once in a year. The effect of this poor interaction is reflected in the poor occurrence of feedback learning, which is needed to optimize channels of information dissemination to subsistence farmers and enhance the robustness of disseminated information. We recommend innovative communication means via mobile phone, promotion of peer-to-peer learning, flexible collaboration relations with more space for feedback from the users of climate information, and more attention to long-term forecasts and their implications for adaptive actions.

Testing “efficient supply chain propositions” using topological characterization of the global supply chain network

In this paper, we study the topological properties of the global supply chain network in terms of its degree distribution, clustering coefficient, degree-degree correlation, bow-tie structure, and community structure to test the efficient supply chain propositions proposed by E. J.S. Hearnshaw et al. The global supply chain data in the year 2017 are constructed by collecting various company data from the web site of Standard & Poor's Capital IQ platform. The in- and out-degree distributions are characterized by a power law of the form of γin = 2.42 and γout = 2.11. The clustering coefficient decays [Formula: see text] with an exponent βk = 0.46. The nodal degree-degree correlations 〈knn(k)〉 indicates the absence of assortativity. The bow-tie structure of giant weakly connected component (GWCC) reveals that the OUT component is the largest and consists 41.1% of all firms. The giant strong connected component (GSCC) is comprised of 16.4% of all firms. We observe that upstream or downstream firms are located a few steps away from the GSCC. Furthermore, we uncover the community structures of the network and characterize them according to their location and industry classification. We observe that the largest community consists of the consumer discretionary sector based mainly in the United States (US). These firms belong to the OUT component in the bow-tie structure of the global supply chain network. Finally, we confirm the validity of Hearnshaw et al.'s efficient supply chain propositions, namely Proposition S1 (short path length), Proposition S2 (power-law degree distribution), Proposition S3 (high clustering coefficient), Proposition S4 ("fit-gets-richer" growth mechanism), Proposition S5 (truncation of power-law degree distribution), and Proposition S7 (community structure with overlapping boundaries) regarding the global supply chain network. While the original propositions S1 just mentioned a short path length, we found the short path from the GSCC to IN and OUT by analyzing the bow-tie structure. Therefore, the short path length in the bow-tie structure is a conceptual addition to the original propositions of Hearnshaw.

Global migration topology analysis and modeling of directed flow network 2006–2010

We applied the network theory to the global world migration phenomenon, seen as a directed network (flow of migrants between world countries from 2006 to 2010) and measured different centralities statistics: in and out-degree, in and out-closeness, and clustering coefficient. One of the important findings is that distributions of out-degree and in-degree for immigration and emigration are completely different aspects of the same phenomenon. The out-degree distribution is uniform with a Gaussian distribution when the in-degree distribution is compound by several groups depending on the in-degree and the in-weight. The receptor countries-nodes, which have large values of in-weight, can be divided into two groups: the developed countries (with low clustering coefficient but large values of the in-degree) and a small group of countries (with high clustering coefficient and small in-degree values). The countries-nodes with large out-weight can be divided into two subgroups with a high clustering coefficient. One of these groups is well connected and forms with the group of the developed countries an in-subgroup of diameter 2 thanks to the double links between them. The second group is characterized by low values of the in-degree (some with null value) and is connected to the rest of the network mainly by out-degrees. Finally, the Latin American countries may be seen as a homogeneous fifth group.

Modeling Network Public Opinion Propagation with the Consideration of Individual Emotions

The occurrence of popular social events causes fluctuations and changes of public emotions, while the rapid development of online social platforms and networks has made individual interactions more intense and further escalated public emotions into public opinion. However, there is a lack of consideration of individual emotions in the current research on online public opinion. Based on this, this paper firstly expounds the quantitative representation of attitude and emotion, analyzes the formation and propagation process of online public opinion by combining individual’s expression willingness, individual’s expression ability, attitude perception value, attitude change probability and other factors, and constructs a network public opinion propagation model that takes individual emotion into consideration. Finally, the main factors affecting the formation and propagation of network public opinion are discussed through simulation experiments. The results demonstrate that: (1) fear is conducive to the formation of online public opinion, but the speed is relatively slow; sadness is not conducive to the formation, but once enough people participate in the exchange of views, the formation of online public opinion will be faster; (2) the influence of online public opinion on individual emotions expands with the increase of the number of individual interactions; (3) different network structures impact differently on the propagation of public opinion. Among them, BA (BA network is a scale-free network model proposed by Barabasi and Albert in order to explain the generation mechanism of power law, BA model has two characteristics: growth and priority connection mechanism) and ER (ER network is a network with random connectivity proposed by Erdös-Renyi) random networks can promote the propagation of online public opinion, which is prone to “one-sided” online public opinion. WS small-world networks (proposed by Watts and Strogatz. It is a kind of network with short average path length and high clustering coefficient) and fully-connected networks have an inhibitory effect on the spread of online public opinion, easily maintaining the multi-dimensional nature of online public opinion.

Network Structure and Performance

AbstractWe develop a theory that links individuals’ network structure to their productivity and earnings. While a higher degree leads to better access to information, more clustering leads to higher peer pressure. Both information and peer pressure affect effort in a model of team production, with each being beneficial in a different environment. We find that information is particularly valuable under high uncertainty, whereas peer pressure is more valuable in the opposite case. We apply our theory to gender disparities in performance. We document the novel fact that men establish more connections (a higher degree) whereas women possess denser networks (a higher clustering coefficient). We therefore expect men to outperform women in jobs that are characterised by high uncertainty in project outcomes and earnings. We provide suggestive evidence that supports our predictions.

Analyzing the structural properties of bike-sharing networks: Evidence from the United States, Canada, and China

Abstract To solve the last-mile problem and promote low carbon transportation, hundreds of cities around the world have launched bike-sharing services. A growing number of studies have been mining bike-sharing data from different cities to understand bike-sharing systems. However, there is still a lack of comprehensive understanding of a bike-sharing network structure. Thus, this paper attempts to use complex network theory and spatial autocorrelation analysis approaches to examine structural properties of bike-sharing systems, quantify the importance of bike stations in the network, and evaluate their spatial clustering patterns. This research analyzes bike-sharing trip data from five different sized bike-sharing systems in the United States, Canada, and China. The results of network analysis reveal that the bike-sharing networks have a small-world property with a small average path length and a high clustering coefficient. Compared with medium-scale networks, the connectivity and accessibility of bike stations are relatively low in the large-scale bike-sharing network. Also, the connectivity of bike stations is positively related to their accessibility while they are not highly correlated with their intermediateness. The spatial clustering analysis results indicate that the spatial distributions of connectivity and accessibility of bike stations have a strong global spatial autocorrelation. Also, the stations with high connectivity and accessibility are concentrated in the urban centers, and the stations with low connectivity and accessibility are clustered in the periphery of the urban areas. However, their intermediateness does not show a strong global spatial clustering pattern, which implies that bike-sharing networks consist of multiple sub-groups. The findings provide new insights for transport planners and managers to understand bike-sharing systems and to improve their service quality.

Altered cortical functional network in drug-naive adult male patients with attention-deficit hyperactivity disorder: A resting-state electroencephalographic study

Relatively little is known about the neurophysiology of adult Attention-deficit/hyperactivity disorder (ADHD). Brain network analysis can yield important insights into the neuropathology in adult ADHD. The objective of this study was to investigate source-level cortical functional network using resting-state electroencephalography (EEG) in drug-naive adult patients with ADHD. Resting-state EEG was performed for 30 adult male patients with ADHD and 27 male healthy controls. Source-level weighted functional networks based on graph theory were evaluated, including strength, clustering coefficient (CC) and path length (PL) in six frequency bands. At the global level, strength (η2 = 0.167) and CC (η2 = 0.156) were lower while PL (η2 = 0.159) was higher for the high beta band in the ADHD patient group compared to healthy controls. At the nodal level, CCs of the high beta band were lower in the left middle temporal gyrus (η2 = 0.244), right inferior occipital cortex (η2 = 0.214), right posterior transverse collateral sulcus (η2 = 0.237), and right anterior occipital sulcus (η2 = 0.251) for the adult ADHD group. Furthermore, the nodal-level high beta band CCs of the left middle temporal gyrus and right anterior occipital sulcus were significantly negatively correlated with ADHD symptoms. The altered cortical functional network showed inefficient connectivity in the left middle temporal gyrus, belonging to the default mode network, the right inferior occipital cortex, belonging to the extrastriate visual resting state network, the right posterior transverse collateral sulcus, belonging to the visual network, and the anterior occipital sulcus, reflecting visual attention, which might affect the pathophysiology of ADHD. Taken together, these attenuated network inefficiencies in adult patients with ADHD may lead to suboptimal information processing and affect symptoms of ADHD, such as inattention and hyperactivity. Our findings should be further replicated using longitudinal study designs.

Hyper-Activated Brain Resting-State Network and Mismatch Negativity Deficit in Schizophrenia With Auditory Verbal Hallucination Revealed by an Event-Related Potential Evidence

Schizophrenia is a holergasia with unclear mechanism and high heterogeneity. Auditory verbal hallucination (AVH) study might help in understanding schizophrenia from the perspective of individual symptoms. This study aimed to investigate the activities of the resting-state networks (RSN) in the electroencephalogram (EEG) and mismatch negativity (MMN) in task-related state of schizophrenia patients with AVH. We recruited 30 schizophrenia patients without any medication for more than 4 weeks (15 AVH patients and 15 Non-AVH patients) and 15 healthy controls. We recorded the EEG data of the participants in the resting-state for 7 min and the event-related potential (ERP) data under an auditory oddball paradigm. In the resting-state EEG network, AVH patients exhibited a higher clustering coefficient than Non-AVH patients and healthy controls on delta and beta bands and a shorter characteristic path length than Non-AVH patients and healthy controls on all frequency bands. For ERP data, AVH patients showed a lower MMN amplitude than healthy controls (p = 0.017) and Non-AVH patients (p = 0.033). What’s more, MMN amplitude was positively correlated with clustering coefficient, and negatively correlated with characteristic path length on delta, theta, beta and gamma band in AVH patients. Our results indicate that AVH patients showed a hyper-activity in resting-state and may have impaired higher-order auditory expectations in the task-related state than healthy controls and Non-AVH patients. And it seems reasonable to conclude that the formation of AVH may occupy certain brain resources and compete for brain resources with external auditory stimuli.

A generalized model for social collaboration networks

In this paper, we constructed a three-parameter general social collaboration network model (GCNM) using both similarity-based strategy and copying-based strategy. In this model, a connection can be introduced between two nodes if they are similar in attributes or similar in structure (i.e., have many common friends). This model can match various types of real-world social networks by just choosing different values for three parameters, and therefore, can reproduce observed real network characteristics. Particularly, three widely studied models (similarity-based, copying-based, and pure preferential attachment (PA)) are only the special cases of this new model. Specifically, this new model possesses following new characteristics which existing models have difficulty to fulfill in all: 1) it not only exhibits the high average clustering coefficient, but also the high global clustering coefficient and explicit community structure (great number of triangles); 2) it not only makes the connections between the new node and existing nodes, but also between existing nodes; and 3) it has not only linear, but also non-linear relationship between the linking probability and the degree (the connectivity of nodes). Numerical results, which are in good agreement with real-world datasets from different fields, demonstrated all of these.

Antiinterference Function of Scale-Free Spiking Neural Network Under AC Magnetic Field Stimulation

The complexity and changeability of electromagnetic environment make the deficiency of traditional methods of electromagnetic protection increasingly prominent. The organisms with the regulation of nervous system have advantages of self-adaptive, self-organizing, and self-repairing. Therefore, it is necessary to explore a new thought on electromagnetic protection by drawing from the biological self-adaptive advantage. In this study, two kinds of scale-free spiking neural networks (sfSNNs) with different clustering coefficients are constructed. Then, the antiinterference function of the sfSNNs under the ac magnetic field stimulation is evaluated and compared. Finally, the antiinterference mechanism is analyzed. The experimental results show that both sfSNNs have a certain antiinterference function, and the performance of the sfSNN with high clustering coefficient is better than that with low clustering coefficient in the antiinterference function; the dynamic evolution of neural information processing in the sfSNN is clarified; and the dynamic regulation of synaptic plasticity is the intrinsic factor of the antiinterference function of the sfSNNs. This study lays a theoretical foundation for the electromagnetic protection of electronic system based on adaptive bionic mechanism.

Determining Exact Solutions for Structural Parameters on Hierarchical Networks With Density Feature

Abstract The problem of determining closed-form solutions for some structural parameters of great interest on networked models is meaningful and intriguing. In this paper, we propose a family of networked models $\mathcal{G}_{n}(t)$ with hierarchical structure where $t$ represents time step and $n$ is copy number. And then, we study some structural parameters on the proposed models $\mathcal{G}_{n}(t)$ in more detail. The results show that (i) models $\mathcal{G}_{n}(t)$ follow power-law distribution with exponent $2$ and thus exhibit density feature; (ii) models $\mathcal{G}_{n}(t)$ have both higher clustering coefficients and an ultra-small diameter and so display small-world property; and (iii) models $\mathcal{G}_{n}(t)$ possess rich mixing structure because Pearson-correlated coefficients undergo phase transitions unseen in previously published networked models. In addition, we also consider trapping problem on networked models $\mathcal{G}_{n}(t)$ and then precisely derive a solution for average trapping time $ATT$. More importantly, the analytic value for $ATT$ can be approximately equal to the theoretical lower bound in the large graph size limit, implying that models $\mathcal{G}_{n}(t)$ are capable of having most optimal trapping efficiency. As a result, we also derive exact solution for another significant parameter, Kemeny’s constant. Furthermore, we conduct extensive simulations that are in perfect agreement with all the theoretical deductions.

Altered Cortical Functional Networks in Patients With Schizophrenia and Bipolar Disorder: A Resting-State Electroencephalographic Study.

BackgroundPathologies of schizophrenia and bipolar disorder have been poorly understood. Brain network analysis could help understand brain mechanisms of schizophrenia and bipolar disorder. This study investigates the source-level brain cortical networks using resting-state electroencephalography (EEG) in patients with schizophrenia and bipolar disorder.MethodsResting-state EEG was measured in 38 patients with schizophrenia, 34 patients with bipolar disorder type I, and 30 healthy controls. Graph theory based source-level weighted functional networks were evaluated: strength, clustering coefficient (CC), path length (PL), and efficiency in six frequency bands.ResultsAt the global level, patients with schizophrenia or bipolar disorder showed higher strength, CC, and efficiency, and lower PL in the theta band, compared to healthy controls. At the nodal level, patients with schizophrenia or bipolar disorder showed higher CCs, mostly in the frontal lobe for the theta band. Particularly, patients with schizophrenia showed higher nodal CCs in the left inferior frontal cortex and the left ascending ramus of the lateral sulcus compared to patients with bipolar disorder. In addition, the nodal-level theta band CC of the superior frontal gyrus and sulcus (cognition-related region) correlated with positive symptoms and social and occupational functioning scale (SOFAS) scores in the schizophrenia group, while that of the middle frontal gyrus (emotion-related region) correlated with SOFAS scores in the bipolar disorder group.ConclusionsAltered cortical networks were revealed and these alterations were significantly correlated with core pathological symptoms of schizophrenia and bipolar disorder. These source-level cortical network indices could be promising biomarkers to evaluate patients with schizophrenia and bipolar disorder.

Using Network Theory to Explore BIM Application Barriers for BIM Sustainable Development in China

Building Information Modeling (BIM) technology has promoted the development of the architecture, engineering, and construction (AEC) industry, but has encountered many barriers to its application in China. Therefore, identifying the barriers to BIM application and capturing their interactions are essential in order to control and eliminate the determined barriers. From this standpoint, 23 BIM application barriers were identified through a literature review and expert interviews. Furthermore, the interactions among them were determined based on the Delphi method, which was the foundation for establishing the BIM application barrier network (BABN). Then, the software Pajek was employed to construct the network model and reveal its topological characteristics based on complex network theory, including degree, betweenness, eigenvector, clustering coefficient, network diameter, and average path length. As indicated by the results, BABN possesses scale-free network property because its cumulative degree distribution obeys power–law distribution. BABN is also a small-world network, due to its relatively high clustering coefficient as well as small average path length, implying that barrier propagation in BABN is fast. In addition, the results are discussed and recommendations are proposed. This research will help BIM stakeholders to develop coping strategies to control and eliminate BIM application barriers for the sake of driving BIM sustainable development.

Optimum topology and coupling strength for synchronization

The category of the small-world networks is neither random (like random networks) nor highly ordered (like regular networks). Their special properties are the combination of high clustering coefficient and short path length which can be seen in many real world networks. Synchronization of a small-world topology of dynamical network receives a great deal of attention in recent years. Here, the synchronization of a small-world network is compared with a regular and random network with the same number of nodes and links. To this end, identical network contains 100 nodes with three different topologies (regular, small-world and random) are considered. The linear stability of the synchronization manifold of these networks is investigated by the help of master stability function approach. Therefore, the synchronization problem is linked to the Laplacian matrix of the network. Through numerical analysis, we show that the optimum coupling strength belongs to the small-world network with proper rewiring probabilities.

Deriving pairwise transfer entropy from network structure and motifs.

Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.

Design of a reservoir for cloud-enabled echo state network with high clustering coefficient

Reservoir computing (RC) is considered as a suitable alternative for descending gradient methods in recursive neural networks (RNNs) training. The echo state network (ESN) is a platform for RC and nonlinear system simulation in the cloud environment with many external users. In the past researches, the highest eigenvalue of reservoir connection weight (spectral radius) was used to predict reservoir dynamics. Some researchers have illustrated; the characteristics of scale-free and small-world can improve the approximation capability in echo state networks; however, recent studies have shown importance of the infrastructures such as clusters and the stability criteria of these reservoirs as altered. In this research, we suggest a high clustered ESN called HCESN that its internal neurons are interconnected in form of clusters. Each of the clusters contains one backbone and a number of local nodes. We implemented a classical clustering algorithm, called K-means, and three optimization algorithms including genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) to improve the clustering efficiency of the new reservoir and compared them with each other. For investigating the spectral radius and predictive power of the resulting reservoirs, we also applied them to the laser time series and the Mackey-Glass dynamical system. It is demonstrated that new clustered reservoirs have some specifications of biologic neural systems and complex networks like average short path length, high clustering coefficient, and power-law distribution. The empirical results illustrated that the ESN based on PSO could strikingly enhance echo state property (ESP) and obtains less chaotic time series prediction error compared with other works and the original version of ESN. Therefore, it can approximate nonlinear dynamical systems and predict the chaotic time series.