Large-degree Nodes Research Articles

A FAST ESTIMATION ALGORITHM OF COMMUNITY NUMBER IN LARGE SCALE-FREE COMPLEX NETWORKS

In conventional community detecting algorithms, the community number is always a bypass product and cannot be estimated before partitioning. Since partitioning large scale and dynamic complex networks takes exhausting computation, the community number sometimes can be a terminal condition of iterations or a preset optimal parameter for speeding up partitioning algorithms. This paper assumes that communities are organized around the center of core nodes in a scale-free network. A separability function is built to dichotomize nodes into two classes and the class of large degree nodes is selected as the core node candidate set. An improved shortest path seeking algorithm is applied to remove the closest neighbors of a specific core node. The number of remaining core nodes is then the estimated number of communities. Experiments of real world scale-free networks and computer generated networks show that the results are very close to the well-proven results.

The different cooperative behaviors on a kind of scale-free networks with identical degree sequence

The power-law degree distribution of scale-free networks plays an important role in the bloom of cooperation in the evolutionary games performed on them. In this paper we apply prisoner’s dilemma and public goods game on a family of scale-free networks with the same degree sequence, and show that power-law behavior alone does not determine the cooperative behavior in scale-free networks. Instead, we present that the direct connections among large-degree nodes have a crucial influence on the evolution of cooperation in the scale-free network family.

Suppressing traffic-driven epidemic spreading by edge-removal strategies

The interplay between traffic dynamics and epidemic spreading on complex networks has received increasing attention in recent years. However, the control of traffic-driven epidemic spreading remains to be a challenging problem. In this Brief Report, we propose a method to suppress traffic-driven epidemic outbreak by properly removing some edges in a network. We find that the epidemic threshold can be enhanced by the targeted cutting of links among large-degree nodes or edges with the largest algorithmic betweenness. In contrast, the epidemic threshold will be reduced by the random edge removal. These findings are robust with respect to traffic-flow conditions, network structures, and routing strategies. Moreover, we find that the shutdown of targeted edges can effectively release traffic load passing through large-degree nodes, rendering a relatively low probability of infection to these nodes.

Scalable community detection in massive social networks using MapReduce

In this paper, we present a community-detection solution for massive-scale social networks using MapReduce, a parallel programming framework. We use a similarity metric to model the community probability, and the model is designed to be parallelizable and scalable in the MapReduce framework. More importantly, we propose a set of degree-based preprocessing and postprocessing techniques named DEPOLD (DElayed Processing of Large Degree nodes) that significantly improve both the community-detection accuracy and performance. With DEPOLD, delaying analysis of 1% of high-degree nodes to the postprocessing stage reduces both processing time and storage space by one order of magnitude. DEPOLD can be applied to other graph-clustering problems. Furthermore, we design and implement two similarity calculation algorithms using MapReduce with different computation and communication characteristics in order to adapt to various system configurations. Finally, we conduct experiments with publicly available datasets. Our evaluation demonstrates the effectiveness, efficiency, and scalability of the proposed solution.

Reverse preferential spread in complex networks

Large-degree nodes may have a larger influence on the network, but they can be bottlenecks for spreading information since spreading attempts tend to concentrate on these nodes and become redundant. We discuss that the reverse preferential spread (distributing information inversely proportional to the degree of the receiving node) has an advantage over other spread mechanisms. In large uncorrelated networks, we show that the mean number of nodes that receive information under the reverse preferential spread is an upper bound among any other weight-based spread mechanisms, and this upper bound is indeed a logistic growth independent of the degree distribution.

Evolutionary games on scale-free networks with tunable degree distribution

We study evolutionary games on scale-free networks with tunable degree distribution. The heterogeneity of networks is controlled by the exponent of power-law degree distribution. It is found that there exists an optimal value of the exponent, for which the level of cooperation becomes highest. This phenomenon indicates that, although degree heterogeneity plays an important role in maintaining cooperation, too strong heterogeneity may counterintuitively encourage defection. We observe that, for strong heterogeneity, large-degree nodes are no longer certainly occupied by cooperators. Our results yield insights into the effect of degree heterogeneity on cooperation.

Diversity-induced resonance on weighted scale-free networks

The diversity-induced resonance in weighted scale-free networks is investigated numerically and analytically. The couplings are weighted according to node degree. It is found that self-organized phase shifts occur between large-degree and small-degree nodes, although there is no time delay in coupling terms. Such spontaneous phase shifts are relevant to the improvement of signal resonance amplification. This finding may help to better understand how the collective behavior of individual units promotes the response of the whole system to external signals.

Molecular Basis for Evolving Modularity in the Yeast Protein Interaction Network

Scale-free networks are generically defined by a power-law distribution of node connectivities. Vastly different graph topologies fit this law, ranging from the assortative, with frequent similar-degree node connections, to a modular structure. Using a metric to determine the extent of modularity, we examined the yeast protein network and found it to be significantly self-dissimilar. By orthologous node categorization, we established the evolutionary trend in the network, from an “emerging” assortative network to a present-day modular topology. The evolving topology fits a generic connectivity distribution but with a progressive enrichment in intramodule hubs that avoid each other. Primeval tolerance to random node failure is shown to evolve toward resilience to hub failure, thus removing the fragility often ascribed to scale-free networks. This trend is algorithmically reproduced by adopting a connectivity accretion law that disfavors like-degree connections for large-degree nodes. The selective advantage of this trend relates to the need to prevent a failed hub from inducing failure in an adjacent hub. The molecular basis for the evolutionary trend is likely rooted in the high-entropy penalty entailed in the association of two intramodular hubs.

Method to enhance traffic capacity for scale-free networks

In this paper, a method is proposed to enhance the traffic handling capacity of scale-free networks by closing or cutting some links between some large-degree nodes, for both local routing strategy and global shortest-path routing strategy. The traffic capacity of networks is found to be considerably improved after applying the link-closing strategy, especially in the case of global routing. Due to the strongly improved network capacity, easy realization on networks, and low cost, the strategy may be useful for modern communication networks.

Multi-degree ROADM based on wavelength selective switches: Architectures and scalability

Multi-degree implementations of the reconfigurable optical add–drop multiplexer (ROADM) are analyzed in terms of in-band crosstalk performance with an emphasis on the reduction in the number of wavelength selective switches used in the module. It is shown experimentally that an 8-degree ROADM using the wavelength selective switches for channel adding and optical splitters for channel dropping performs closely to one that uses switches for both operations. A new modular architecture based on the wavelength selective switches is proposed for implementations applicable to large degree nodes. Performance analysis of this architecture indicates node scalability to 256 degree with crosstalk-induced power penalties below 0.5 dB.

Empirical study of Chinese city airline network

We investigate the empirical properties of Chinese city airline network, where nodes and edges denote cities and direct fights. The present network is a small-world network with short average path length and high degree of clustering, and its degree distribution follows a double power law. The degree-degree correlation of the present network is different from that of the world airport network and the North American air network: The small-degree nodes of the world airport network and the North American air network are positively correlated, whereas those of the present network don't exhibit correlation behavior. And for large-degree nodes, the average neighboring degrees approach a constant in the world airport network, while the present network shows negatively correlated behavior. Previous studies suggested the absence of hierarchical structure in geographical networks, such as the Internet, the electrical power grids, and so on. However, the present network displays an obviously hierarchical property, which provides us an evidence that the geographical ingredient may have no effect on the structural evolution of Chinese city airline network. Furthermore, by setting the number of available seats per week as the edge weight, we investigate the correlation between weight and degree, and find a power-law weight-degree correlation with exponent 1.37.

Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity

In this paper, we propose a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate. Furthermore, by numerical simulation, we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible-infected model. Finally, we investigate a fast spreading strategy when only local information is available. Different from the extensively studied path-finding strategy, the strategy preferring small-degree nodes is more efficient than that preferring large-degree nodes. Our results indicate the existence of an essential relationship between network traffic and network epidemic on scale-free networks.