Average Degree Of Network Research Articles

Spike-timing-dependent plasticity optimized coherence resonance and synchronization transitions by autaptic delay in adaptive scale-free neuronal networks

In this paper, we numerically study the effect of spike-timing-dependent plasticity on multiple coherence resonance and synchronization transitions induced by autaptic time delay in adaptive scale-free Hodgkin–Huxley neuron networks. As the adjusting rate Ap of spike-timing-dependent plasticity increases, multiple coherence resonance and synchronization transitions enhance and become strongest at an intermediate Ap value, indicating that there is optimal spike-timing-dependent plasticity that can most strongly enhance the multiple coherence resonance and synchronization transitions. As Ap increases, increasing network average degree has a small effect on multiple coherence resonance, but its effect on synchronization transitions changes from suppressing to enhancing it. As network size is varied, multiple coherence resonance and synchronization transitions nearly do not change. These results show that spike-timing-dependent plasticity can simultaneously optimize multiple coherence resonance and synchronization transitions by autaptic delay in the adaptive scale-free neuronal networks. These findings provide a new insight into spike-timing-dependent plasticity and autaptic delay for the information processing and transmission in neural systems.

Interlocking directorates and different power forms: An explorative analysis in the Italian context

The purpose of the present paper is twofold. The first is to update the contribution by Drago et al. (2011) about cross-shareholdings and interlocking directorates in Italian listed companies (FTSE MIB) to 31 December 2016 and to reinforce theory of enlarged collusion. The second is to find how interlocking directorates can contribute to understanding the power structure. By using the social network analysis, we map the network structure of interlocking boards and employ centrality measures like degree, eigenvector and betweenness centrality along with the network density and average degree. We interpret eigenvector centrality as a measure of “effective power” of the connections because it can be seen as a weighted sum of not only direct connections but indirect connections, while betweenness centrality as a measure of “potential power” because it is a proxy of the volume of information that passes through the nodes. In this way, we provide a framework for selecting Italian firms with effective and potential power – around whom interactions and processes can be traced and analysed. In addition, we find that the position assumed by the controlling group of the Mediobanca Galaxy is definitely downsized.

Coordination on Networks

We study a coordination game among agents on a network, who choose whether or not to take an action in an uncertain environment that yields value increasing in the actions of neighbors. We develop an algorithm that fully characterizes the equilibrium partitions (coordination sets) and thresholds using the primitives of the model. We show that there is a single coordination set if and only if the network is balanced, i.e., the average degree of each subnetwork is no larger than the average degree of the network. Comparative statics exercises as well as welfare properties are investigated. In particular, we show that contagion is localized within coordination sets. Compared to the perfect information case, both the equilibrium selection, the comparative statics properties as well as the policy implications are different.

Emergence of cooperation in a coupled socio-ecological system through a direct or an indirect social control mechanism

The successful management of a common pool resource (CPR) by its social agents is key to its sustainability. In order to maintain the ecological resource of such a coupled socio-ecological system, cooperative effort from the whole society is required and this necessitates proper social control mechanism to regulate the social order. In this paper, we explore the effects of two social control mechanisms: ostracism and voluntary enforcement, on agents that actively exploit the CPR within societies of different social network structures (as encapsulated by its average network degree). By means of numerical simulations and analytical approximation, we made inference on the dynamical behavior of the system in terms of its phase diagram. The phase diagram is found to contain a plethora of phases and associated phase transitions as we enumerate them based on a social and an ecological parameter. At a large average network degree, the features of the phases are observed to be similar for the direct voluntary enforcement and indirect ostracism mechanisms. However, these features exhibit a unique difference at low average network degree, where we uncover a new phenomenon of non-equilibrium oscillatory phase attributed to the voluntary enforcement mechanism.

Transmission network structure and newly diagnosed HIV infections: a molecular epidemiology study

BackgroundImproved understanding of network structure—one of the driving forces of HIV transmission—could facilitate the design of interventions. We aimed to assess the structure of HIV transmission networks and their relationship to newly diagnosed cases in Hong Kong, where sexual transmission between men prevails. MethodsWe used HIV gag-pol sequences collected over a 20-year period from all major HIV services in Hong Kong to construct transmission networks. We identified network clusters and decomposed them by modularity if one contained more than half of the connected nodes. We analysed network size, average degree, and epidemiological metrics, and examined sequences of newly diagnosed cases in a cross-sectional study to assess growth of identified clusters. FindingsA total of 2352 archived HIV sequences collected in 1994–2013 were retrieved, alongside HIV sequences from 81 cases diagnosed between Aug 4, 2016, and Jan 17, 2017. The transmission network with a density of 1·58% contained 1801 (74%) nodes that were linked to at least one other node. Network degree followed a power law distribution (correlation 0·988). There were 72 dyads and 64 clusters with at least three nodes. The largest connected component contained more than half of the connected nodes (1282 [71%]) and thus was decomposed into 20 clusters. Of 83 clusters included in the analysis, 10 were linked to 37 (46%) new cases. The sizes of incident clusters were significantly larger (p<0·001, median 15 [IQR 11-81] vs 4 [IQR 3-8]) with a higher mean degree (p<0·001, 10·86 [IQR 4·35–22·64] vs 2·80 [IQR 2·00–4·64]). Clusters with newly diagnosed patients had higher transmission speeds (p<0·001, median 0·97 [IQR 0·72–4·77] persons per year [ppy] vs 0·24 [IQR 0·17–0·44] ppy). Clusters with new cases in 2016 had a higher 3-year cluster incidence in 2013 (p<0·001, 0·33 [IQR 0·33–4·17]) and wider age difference between nodes (40·50 years [IQR 24·75–50·25]) than those without new cases in 2016 (3-year cluster incidence 0·00 [IQR 0·00–0·33]; age difference 17·00 years [IQR 10·00–28·5]). InterpretationHong Kong's HIV transmission was a preferential attachment process as inferred from the power law degree distribution elicited. The HIV epidemic has grown from existing clusters with large size, degree, and transmission speed. Disassortative age mixing could have predisposed younger individuals to transmission risk from older patients. FundingResearch Grants Council of Hong Kong (14103315), AIDS Trust Fund (MSS 229 R, 243 R).

Temporal Coherence Transitions Induced by Channel Noise in Scale-Free Neuronal Networks with Time Delay

In this paper, we study the effect of channel noise on the temporal coherence of scale-free Hodgkin–Huxley neuronal networks with time delay. It is found that the temporal coherence of the neuronal networks changes as channel noise intensity is varied in different ways depending on the range of channel noise intensity. The temporal coherence monotonically decreases with the increase of channel noise intensity for too small or too big channel noise intensity. However, for intermediate channel noise intensity it intermittently and rapidly becomes high and low as channel noise intensity is varied, exhibiting temporal coherence transitions. Moreover, this phenomenon is dependent on coupling strength and network average degree and becomes strongest when they are optimal. This result shows that channel noise has a regulation effect on the temporal coherence of the delayed neuronal networks by inducing temporal coherence transitions. This provides a new insight into channel noise for the information processing and transmission in neural systems.

Optimized design and availability analysis of large-scale shared backup path protected networks

Traditional integer linear programming model for shared backup path networks allows only one working route and one backup route per demand and does not scale well. By introducing multiple working routes and backup routes, the traditional multi-flow model solves in a faster manner. This paper seeks improvements on the traditional multi-flow model and develops an algorithm to assess availability for multi-flow shared backup path protection models. Experiments on 165 networks testify that the newly proposed model is 51% faster on average with similar total cost and overall network availability, compared with the traditional multi-flow model. All the networks in this paper are designed to be 100% single-failure restorable, and major findings regarding these networks include: (1) total cost of assigning backup capacity to each span dwindles away with increasing network average nodal degree; (2) network availability first rises then falls as network average nodal degree increases; and (3) when network scale increases, network availability decreases with fluctuations. The results found are explained with two case studies in this paper.

Controllability of social networks and the strategic use of random information

BackgroundThis work is aimed at studying realistic social control strategies for social networks based on the introduction of random information into the state of selected driver agents. Deliberately exposing selected agents to random information is a technique already experimented in recommender systems or search engines, and represents one of the few options for influencing the behavior of a social context that could be accepted as ethical, could be fully disclosed to members, and does not involve the use of force or of deception.MethodsOur research is based on a model of knowledge diffusion applied to a time-varying adaptive network and considers two well-known strategies for influencing social contexts: One is the selection of few influencers for manipulating their actions in order to drive the whole network to a certain behavior; the other, instead, drives the network behavior acting on the state of a large subset of ordinary, scarcely influencing users. The two approaches have been studied in terms of network and diffusion effects. The network effect is analyzed through the changes induced on network average degree and clustering coefficient, while the diffusion effect is based on two ad hoc metrics which are defined to measure the degree of knowledge diffusion and skill level, as well as the polarization of agent interests.ResultsThe results, obtained through simulations on synthetic networks, show a rich dynamics and strong effects on the communication structure and on the distribution of knowledge and skills.ConclusionsThese findings support our hypothesis that the strategic use of random information could represent a realistic approach to social network controllability, and that with both strategies, in principle, the control effect could be remarkable.

Channel noise-induced temporal coherence transitions and synchronization transitions in adaptive neuronal networks with time delay

Using spike-timing-dependent plasticity (STDP), we study the effect of channel noise on temporal coherence and synchronization of adaptive scale-free Hodgkin-Huxley neuronal networks with time delay. It is found that the spiking regularity and spatial synchronization of the neurons intermittently increase and decrease as channel noise intensity is varied, exhibiting transitions of temporal coherence and synchronization. Moreover, this phenomenon depends on time delay, STDP, and network average degree. As time delay increases, the phenomenon is weakened, however, there are optimal STDP and network average degree by which the phenomenon becomes strongest. These results show that channel noise can intermittently enhance the temporal coherence and synchronization of the delayed adaptive neuronal networks. These findings provide a new insight into channel noise for the information processing and transmission in neural systems.

Cascading failure model of scale-free topology for avoiding node failure

In order to efficiently fortify the robustness of a scale-free network against cascading failure, a model of this phenomenon is proposed based on defining the load of a node with respect to both degree and betweenness centrality. Simultaneously, when the load is redistributed, an allocation proportion is ascertained according to both the loads and the energies of the nodes. After that, we obtain the relationship between the model parameters and the robustness of the network against the cascading failure with theoretical analysis, which also helps us determine the influence of the average network degree on cascading failure. Finally, the results of theoretical analysis are verified with simulation experiments.

Microbial diversity and ecological networks as indicators of environmental quality

Evaluating the quality of ecosystems in terms of biological patrimony and functioning is of critical importance in the actual context of intensified human activities. Microbial diversity is commonly used as a bioindicator of ecosystems functioning. However, there is a lack of sensitivity of microbial diversity indicators in the case of moderate and chronic environmental degradation, such as atmospheric deposition of pollutants, agricultural practices, diffuse pollution by wastewater and climate change. As a consequence, there is a need for alternative bioindicators of soils and water quality. Here, we discuss the interest of adopting a more integrative approach based on biotic interaction networks beyond the simple diversity indicators. We review how the various biotic interactions can be integrated in the various microbial networks such as trophic, mutualistic and co-occurrence networks. Then we discuss the efficiency of microbial networks and associated metrics to detect changes in microbial communities. We conclude that the connectance, the number of links and the average degree of co-occurrence networks could vary from 10 to 50% in response to minor perturbations when microbial diversity parameters remain stable. Finally, we analyze studies that aimed at linking microbial networks and activity to evaluate the potential of such networks for providing simple and operational indicators of ecosystem quality and functioning.

Efficient calculation of the robustness measure [formula omitted] for complex networks

In a recent work, Schneider et al. (2011) proposed a new measure R for network robustness, where the value of R is calculated within the entire process of malicious node attacks. In this paper, we present an approach to improve the calculation efficiency of R, in which a computationally efficient robustness measure R′ is introduced when the fraction of failed nodes reaches to a critical threshold qc. Simulation results on three different types of network models and three real networks show that these networks all exhibit a computationally efficient robustness measure R′. The relationships between R′ and the network size N and the network average degree 〈k〉 are also explored. It is found that the value of R′ decreases with N while increases with 〈k〉. Our results would be useful for improving the calculation efficiency of network robustness measure R for complex networks.

Structural Analysis of Bus Networks Using Indicators of Graph Theory and Complex Network Theory

The structure of bus network is very significant for bus system. To evaluate the performance of the structure of bus network, indicators basing on graph theory and complex network theory are proposed. Three forms of matrices comprising line-station matrix, weighted adjacency matrix and adjacency matrix under space P are used to represent the bus network. The paper proposes a shift power law distribution which is related average degree of network to fit the degree distribution and a method to calculate the average transfer time between any two stations using adjacency matrix under P space. Moreover, this paper proposes weighted average shortest path distance and transfer efficiency to evaluate the bus network. The results show that the indicators that we introduce, effectively reflect properties of bus network.

Multiple coherence resonances and synchronization transitions by time delay in adaptive scale-free neuronal networks with spike-timing-dependent plasticity

In this paper, we numerically study the effect of spike-timing-dependent plasticity (STDP) on multiple coherence resonances (MCR) and synchronization transitions (ST) induced by time delay in adaptive scale-free Hodgkin–Huxley neuronal networks. It is found that STDP has a big influence on MCR and ST induced by time delay and on the effect of network average degree on the MCR and ST. MCR is enhanced or suppressed as the adjusting rate Ap of STDP decreases or increases, and there is optimal Ap by which ST becomes strongest. As network average degree 〈k〉 increases, ST is enhanced and there is optimal 〈k〉 at which MCR becomes strongest. Moreover, for a larger Ap value, ST is enhanced more rapidly with increasing 〈k〉 and the optimal 〈k〉 for MCR increases. These results show that STDP can either enhance or suppress MCR, and there is optimal STDP that can most strongly enhance ST induced by time delay in the adaptive neuronal networks. These findings could find potential implication for the information processing and transmission in neural systems.

Epileptic seizure onset correlates with long term EEG functional brain network properties.

We investigated the correlation of epileptic seizure onset times with long term EEG functional brain network properties. To do so, we constructed binary functional brain networks from long-term, multichannel electroencephalographic data recorded from nine patients with epilepsy. The corresponding network properties were quantified using the average network degree. It was found that the network degree (as well as other network properties such as the network efficiency and clustering coefficient) exhibited large fluctuations over time; however, it also exhibited specific periodic temporal structure over different time scales (1.5hr-24hr periods) that was consistent across subjects. We investigated the correlation of the phases of these network periodicities with the seizure onset by using circular statistics. The results showed that the instantaneous phases of the 3.5hr, 5.5hr, 12hr and 24hr network degree periodic components are not uniformly distributed, suggesting that functional network properties are related to seizure generation and occurrence.

A Depth-Adjustment Deployment Algorithm Based on Two-Dimensional Convex Hull and Spanning Tree for Underwater Wireless Sensor Networks.

Most of the existing node depth-adjustment deployment algorithms for underwater wireless sensor networks (UWSNs) just consider how to optimize network coverage and connectivity rate. However, these literatures don’t discuss full network connectivity, while optimization of network energy efficiency and network reliability are vital topics for UWSN deployment. Therefore, in this study, a depth-adjustment deployment algorithm based on two-dimensional (2D) convex hull and spanning tree (NDACS) for UWSNs is proposed. First, the proposed algorithm uses the geometric characteristics of a 2D convex hull and empty circle to find the optimal location of a sleep node and activate it, minimizes the network coverage overlaps of the 2D plane, and then increases the coverage rate until the first layer coverage threshold is reached. Second, the sink node acts as a root node of all active nodes on the 2D convex hull and then forms a small spanning tree gradually. Finally, the depth-adjustment strategy based on time marker is used to achieve the three-dimensional overall network deployment. Compared with existing depth-adjustment deployment algorithms, the simulation results show that the NDACS algorithm can maintain full network connectivity with high network coverage rate, as well as improved network average node degree, thus increasing network reliability.

Social network structures and bank runs

This paper investigates the impact of social network structures of depositors on bank runs. The analyzed network structures include random networks, small-world networks and scale-free networks. Simulation results show that the probability of bank run occurrence in random networks is larger than that in small-world networks, but the probability of bank run occurrence in scale-free networks drops from the highest to the lowest among the three types of network structures with the increase of the proportion of impatient depositors. The average degree of depositor networks has a significant impact on bank runs, but this impact is related to the proportion of impatient depositors and the confidence levels of depositors in banks.

Degree distribution of random birth-and-death network with network size decline**Project supported by the National Natural Science Foundation of China (Grant No. 61273015) and the Chinese Scholarship Council.

In this paper, we provide a general method to obtain the exact solutions of the degree distributions for random birth-and-death network (RBDN) with network size decline. First, by stochastic process rules, the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 < p < 1/2, then the average degree of network with n nodes is introduced to calculate the degree distributions. Specifically, taking m = 3 for example, we explain the detailed solving process, in which computer simulation is used to verify our degree distribution solutions. In addition, the tail characteristics of the degree distribution are discussed. Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.

C-POEM: comprehensive performance optimization evaluation model for wireless sensor networks

Performance optimization is one of the core issues in wireless sensor networks (WSNs). The existing efforts on performance optimization mainly consist of two research themes: power control and sleep scheduling. A well-designed network performance optimization method is not only close to the actual but also has good generality. There are many aspects that need to be studied. This paper aims to pursue a trade-off between network comprehensive performance and survival time by employing gain and cost to characterize the whole network performance. Towards this goal, a comprehensive performance optimization evaluation model based on complex network theory is proposed. In addition, a relevant optimization algorithm is proposed, which bears a number of merits such as low complexity and competitive performance. Simulation results show that WSNs have the best network average degree to make network obtain maximum income.

Minimal set of nodes to control the dynamics of biological neuronal networks

Controlling the dynamics of biological neuronal network (BNNs) is of great importance for both understanding the brain and for developing means to control brain disease related aberrant activity. In the last decade, the relationship among node properties, network structure and network dynamics has become clearer and several neuron and network properties could be used to control the network dynamics. Designing appropriate control inputs would require selective manipulation of the control variable in each node. However, the large size of BNNs and scarcity of resources do not allow control of all individual nodes by external means. Therefore, there is a need to identify a much smaller number of influential nodes that are sufficient to drive the activity dynamics of the entire BNN to a desired state. Here, we used the concept of structural controllability [1] to identify a small set of influential nodes, control nodes, for synthetic and experimental networks. The later includes large-scale connectivity of macaque cortical regions [2], meso-scale connectome of a mouse brain [3] and the neuronal connectivity of C. elegans [4]. We investigated the effect of random and systematic edge pruning on the number of these control nodes. Moreover, We showed that there is a power law or exponential dependence between the number of control nodes and the average degree of many networks. Finally, we used a simplified network of the basal ganglia to qualitatively show that few control nodes can indeed drive the network dynamics to a desired state. While every sub-network could be used as a control node or sensor, each node is different in terms of the required stimulation pattern, stimulation energy and time to reach the desired dynamical state.