Node Degree Distribution Research Articles

Punishment Leads to Cooperative Behavior in Structured Societies

Altruistic punishment occurs when an agent incurs a cost to punish another but receives no material benefit for doing so. Despite the seeming irrationality of such behavior, humans in laboratory settings routinely pay to punish others even in anonymous, one-shot settings. Costly punishment is ubiquitous among social organisms in general and is increasingly accepted as a mechanism for the evolution of cooperation. Yet if it is true that punishment explains cooperation, the evolution of altruistic punishment remains a mystery. In a series of computer simulations I give agents the ability to punish one another while playing a continuous prisoner's dilemma. In simulations without social structure, expected behavior evolves-agents do not punish and consequently no cooperation evolves. Likewise, in simulations with social structure but no ability to punish, no cooperation evolves. However, in simulations where agents are both embedded in a social structure and have the option to inflict costly punishment, cooperation evolves quite readily. This suggests a simple and broadly applicable explanation of cooperation for social organisms that have nonrandom social structure and a predisposition to punish one another. Results with scale-free networks further suggest that nodal degree distribution plays an important role in determining whether cooperation will evolve in a structured population.

The impact of multi‐group multi‐layer network structure on the performance of distributed consensus building strategies

SUMMARYWe consider a structural approach to the consensus building problem in multi‐group multi‐layer (MGML) distributed sensor networks (DSNs) common in many natural and engineering applications. From among the possible network structures, we focus on bipartite graph structure as it represents a typical MGML structure and has a wide applicability in the real world. We establish exact conditions for consensus and derive a precise relationship between the consensus value and the degree distribution of nodes in a bipartite MGML DSN. We also demonstrate that for subclasses of connectivity patterns, convergence time and simple characteristics of network topology can be captured by explicit algebra. Direct inference of the convergence behavior of consensus strategies from MGML DSN structure is the main contribution of this paper. The insights gained from our analysis facilitate the design and development of large‐scale DSNs that meet specific performance criteria. Copyright © 2012 John Wiley & Sons, Ltd.

Directed-Weighted Modeling of Resource Node in Manufacturing Grid and Its Application Analysis

Complex network has penetrated into numerous fields including mathematics and sciences, life science and engineering discipline, with strong interdisciplinary features. This paper applies the complex network theory into Manufacturing Grid field by abstracting multi-node network in Manufacturing Grid into complex network. Firstly, the characteristics of the direction and weight of the resource node in Manufacturing Grid are analyzed. Then, complex network modeling of resource nodes in Manufacturing Grid is launched. Some possible application such as node degree, shortest path between two nodes and role of node are discussed. Finally, typical examples of complex network, for example, the distribution of resource node degree and the shortest path between manufacturing subtasks are provided. The work of the paper supplies a new sight and approach to the research and study on Manufacturing Grid.

Research on Engineering Software Data Formats Conversion Network

Disperse engineering information constitutes a domain of complex relationship, into which researching with complex network could contribute significantly to its organization and preservation. A complex network which takes engineering software data formats as nodes is constructed and its statistical characteristics, such as directed edge or undirected edge, the node number, the edge number, average path length, clustering coefficient and node degree distribution, etc, are analyzed in this paper. A Voronoi diagram based complex network visualization and retrieval method is provided. According to statistical characteristics of constructed network, visualization method calculates network nodes’ position in a two-dimensional plane and divides this plane into Voronoi diagram by feature nodes of network nodes’ clustering and network nodes. Retrieval method restricts compared nodes to nodes in Voronoi domain of feature nodes which are more related to query node, the number of compared nodes is reduced in retrieval process. The experiment result indicates applying this method into data formats conversion path retrieval can ensure retrieval precision and improve retrieval efficiency, thus provide reliable basis for migrating numerous disperse engineering information.

The severity of mental disorders is linked to interaction among candidate genes

There is a considerable overlap in the manifestation of symptoms in three mental disorders namely unipolar disorder, bipolar disorder and schizophrenia. A gene coexpression network was developed based on a mutual information approach including four candidate genes (NRG1, DISC1, BDNF and COMT) along with other coexpressing genes in unipolar disorder, bipolar disorder and schizophrenia. There is a significant difference in the degree distribution of nodes between normal and bipolar disorder network and bipolar disorder network and schizophrenia network. Moreover, there is a differential direct connectivity among candidate genes in various mental disorders and between normal and mental disorders. All candidate genes are directly connected to each other in schizophrenia except one pair (NRG1-BDNF) indicating a strong role of inter-gene interactions in the manifestation of severe symptoms in this disease. DISC1 and NRG1 are key hub genes in the unipolar disorder network and the bipolar disorder network but have lost the role of hub genes in schizophrenia network, despite their significant association with schizophrenia. This study indicates that the three psychiatric diseases may not have discrete classes but three phenotypic manifestations of the same continuous disease based on severity.

Analysis on topological properties of Beijing urban public transit based on complex network theory

To analyze the topological properties of Beijing public transport network, until July 2010, we have collected 1165 bus lines and 9618 bus stops of Beijing City (14 districts and 2 counties) as the sample data to build up a directed and weighted complex network model based on neighboring stops by applying the complex network theory. In this model, bus stops are considered as nodes of the complex network, while bus lines connecting two neighboring stops as edges. Consequently, the network has the topological properties of a complex network and meanwhile the nodes (bus stops) have clear geographic coordinates. The complexity of Beijing public transport is then verified through analyzing the topological properties of node degree, node strength, strength distribution, average shortest path, clustering coefficient in the complex network. We find that the distributions of node degrees and node strengths are extremely uneven and the cumulative strength distributions of the top 5% and 10% nodes reach 22.43% and 43.02% respectively. The results also show that the node strength, ordinal number and cumulative strength distribution of the nodes all follow the power-law distribution, showing the network characteristics of scale-free and small world. Some "key nodes" play an important role in network connection. We find two kinds of "key nodes" by using high carrying pressure node analysis and extract regional central analysis. These rules provide new references for optimizing the urban transport network, managing traffic congestion and planning and developing the traffic.

On the characterisation of vehicular mobility in a large-scale public transport network

In this paper, we present a thorough characterisation of the spatio–temporal communication graph of a large–scale real–world public transport network. Unlike previous studies, which either use synthetic mobility traces or data from small networks (< 50 nodes), our analysis is based on the mobility patterns of a large–scale (∼1200 nodes) real–world public transport network. In particular, we examine the node degree distribution, encounter patterns, periodicity and clustering behaviour - properties that are particularly relevant in the context of data forwarding in DTN. Our extensive study demonstrates that public transport networks exhibit repetitive patterns and corroborates the existence of few highly connected nodes (termed as hubs). We have also found that the degree distribution of nodes and the inter–contact durations follow the properties of power–law distributions and exhibit moderate to strong self–similarities. We provide insights on how these properties can be leveraged to design effective communication protocols for such large–scale DTN.

Evolving Model for the Complex Traffic and Transportation Network Considering Self‐Growth Situation

It has been approved that the scale‐free feature exists in various complex networks, such as the internet, the cell or the biological networks. In order to analyze the influence of the self‐growth phenomenon during the growth on the structure of traffic and transportation network, we formulated an evolving model. Based on the evolving model, we prove in mathematics that, even that the self‐growth situation happened, the traffic and transportation network owns the scale‐free feature due to that the node degree follows a power‐law distribution. A real traffic and transportation network, China domestic airline network is tested to consolidate our conclusions. We find that the airline network has a node degree distribution equivalent to the power‐law of which the estimated scaling parameter is about 3.0. Moreover the standard error of the estimated scaling parameter changes according to the self‐growth probability. Our findings could provide useful information for determining the optimal structure or status of the traffic and transportation network.

Towards Unbiased BFS Sampling

Breadth First Search (BFS) is a widely used approach for sampling large graphs. However, it has been empirically observed that BFS sampling is biased toward high-degree nodes, which may strongly affect the measurement results. In this paper, we quantify and correct the degree bias of BFS. First, we consider a random graph RG(pk) with an arbitrary degree distribution pk. For this model, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction f of covered nodes. We also show that, for RG(pk), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, Snowball Sampling, RDS) have exactly the same bias. Next, we propose a practical BFS-bias correction procedure that takes as input a collected BFS sample together with the fraction f. Our correction technique is exact (i.e., leads to unbiased estimation) for RG(pk). Furthermore, it performs well when applied to a broad range of Internet topologies and to two large BFS samples of Facebook and Orkut networks.

Visualization and Analysis of the Complexome Network of Saccharomyces cerevisiae

Most processes in the cell are delivered by protein complexes, rather than individual proteins. While the association of proteins has been studied extensively in protein-protein interaction networks (the interactome), an intuitive and effective representation of complex-complex connections (the complexome) is not yet available. Here, we describe a new representation of the complexome of Saccharomyces cerevisiae. Using the core-module-attachment data of Gavin et al. ( Nature 2006 , 440 , 631 - 6 ), protein complexes in the network are represented as nodes; these are connected by edges that represent shared core and/or module protein subunits. To validate this network, we examined the network topology and its distribution of biological processes. The complexome network showed scale-free characteristics, with a power law-like node degree distribution and clustering coefficient independent of node degree. Connected complexes in the network showed similarities in biological process that were nonrandom. Furthermore, clusters of interacting complexes reflected a higher-level organization of many cellular functions. The strong functional relationships seen in these clusters, along with literature evidence, allowed 44 uncharacterized complexes to be assigned putative functions using guilt-by-association. We demonstrate our network model using the GEOMI visualization platform, on which we have developed capabilities to integrate and visualize complexome data.

基于复杂网络的操作系统内核演化与稳定性研究

This paper presents a novel method to study Linux kernel evolution using complex networks. Having investigated the node degree distribution and average path length of the call graphs corresponding to the kernel modules of 223 different versions (V1.1.0 to V2.4.35), we found that the call graphs are scale-free and small-world networks. Based on the relationship between average path length and nodes, we propose a method to find unusual points during Linux kernel evolution using the slope of the average path length. Using the unusual points we identify major structural changes in kernel modules. A stability coefficient is also proposed to describe quantitatively the stability of kernel modules during evolution. Finally, we verify our result through Vasas metrics method.

Evolution and stability of Linux kernels based on complex networks

This paper presents a novel method to study Linux kernel evolution using complex networks. Having investigated the node degree distribution and average path length of the call graphs corresponding to the kernel modules of 223 different versions (V1.1.0 to V2.4.35), we found that the call graphs are scale-free and smallworld networks. Based on the relationship between average path length and nodes, we propose a method to find unusual points during Linux kernel evolution using the slope of the average path length. Using the unusual points we identify major structural changes in kernel modules. A stability coefficient is also proposed to describe quantitatively the stability of kernel modules during evolution. Finally, we verify our result through Vasa’s metrics method.

A Complete Spectrum Sensing and Sharing Model for Cognitive Radio Ad Hoc Wireless Networks Using Markov Chain State Machine

an unlimited number of secondary users. It includes the sharing aspect of Cognitive Radio. Power-law distribution of node degree in scale-free networks is important for considering the traffic distribution and resource management thus we consider the effect of the topology on sensing and sharing performances. The authors demonstrate that CIF outperforms Uniform Indexing (UI) algorithm in Scale-Free networks while in Random networks UI performs as well as CIF.

Entropic equation of state and scaling functions near the critical point in uncorrelated scale-free networks

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent λ appears to be a global variable and plays a crucial role, similar to the dimensionality d for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.

An Analytical Model for the Node Degree in Wireless Ad Hoc Networks

Node degree is regarded as an important and convenient metric to measure the connectivity of wireless ad hoc networks. Existing studies are mainly based on the assumption that nodes are static and do not provide closed-form expressions for node degree. In this paper, we investigate three fundamental characteristics of a wireless ad hoc network: Its node degree distribution, its average node degree and its maximum node degree experienced by the nodes during their movement. We introduce a novel mathematical model to derive analytical expressions in the presence of radio channel fading. Furthermore, our results reveal that the node degree distribution follows a binomial distribution regardless of the initial distribution of nodes’ location. The results of this paper are useful to study node connectivity and to improve the algorithmic complexity of incentive protocols.

Network statistical analysis in peer-to-peer application

The rich statistical characteristics in peer-to-peer (p2p) network have recently attracted much research interest. This paper reveals the internal network statistical characteristics in the user network and resource network, both of which are abstracted from the real application downloading logs. The two-segment degree and weight distribution of user nodes indicate the dynamic of p2p users, and the similar power-law distribution of resource nodes shows the popularity diversity. Furthermore, we found that these two networks have the inherent cluster structure, only minority of clusters contain a large number of nodes, and the majority have fewer nodes in it. In user network, users in the same cluster have similar file-sharing interest, in contrast to the different user interest between clusters; meanwhile, there are obvious correlations between different resource categories in resource clusters.

Improved Construction of Irregular Progressive Edge-Growth Tanner Graphs

The progressive edge-growth algorithm is a well-known procedure to construct regular and irregular low-density parity-check codes. In this paper, we propose a modification of the original algorithm that improves the performance of these codes in the waterfall region when constructing codes complying with both, check and symbol node degree distributions. The proposed algorithm is thus interesting if a family of irregular codes with a complex check node degree distribution is used.

Rewiring dynamical networks with prescribed degree distribution for enhancing synchronizability

In this paper, we present an algorithm for enhancing synchronizability of dynamical networks with prescribed degree distribution. The algorithm takes an unweighted and undirected network as input and outputs a network with the same node-degree distribution and enhanced synchronization properties. The rewirings are based on the properties of the Laplacian of the connection graph, i.e., the eigenvectors corresponding to the second smallest and the largest eigenvalues of the Laplacian. A term proportional to the eigenvectors is adopted to choose potential edges for rewiring, provided that the node-degree distribution is preserved. The algorithm can be implemented on networks of any sizes as long as their eigenvalues and eigenvectors can be calculated with standard algorithms. The effectiveness of the proposed algorithm in enhancing the network synchronizability is revealed by numerical simulation on a number of sample networks including scale-free, Watts-Strogatz, and Erdős-Rényi graphs. Furthermore, a number of network's structural parameters such as node betweenness centrality, edge betweenness centrality, average path length, clustering coefficient, and degree assortativity are tracked as a function of optimization steps.

Understanding overlay characteristics of a large-scale peer-to-peer IPTV system

This article presents results from our measurement and modeling efforts on the large-scale peer-to-peer (p2p) overlay graphs spanned by the PPLive system, the most popular and largest p2p IPTV (Internet Protocol Television) system today. Unlike other previous studies on PPLive, which focused on either network-centric or user-centric measurements of the system, our study is unique in (a) focusing on PPLive overlay-specific characteristics, and (b) being the first to derive mathematical models for its distributions of node degree, session length, and peer participation in simultaneous overlays. Our studies reveal characteristics of multimedia streaming p2p overlays that are markedly different from existing file-sharing p2p overlays. Specifically, we find that: (1) PPLive overlays are similar to random graphs in structure and thus more robust and resilient to the massive failure of nodes, (2) Average degree of a peer in the overlay is independent of the channel population size and the node degree distribution can be fitted by a piecewise function, (3) The availability correlation between PPLive peer pairs is bimodal, that is, some pairs have highly correlated availability, while others have no correlation, (4) Unlike p2p file-sharing peers, PPLive peers are impatient and session lengths (discretized, per channel) are typically geometrically distributed, (5) Channel population size is time-sensitive, self-repeated, event-dependent, and varies more than in p2p file-sharing networks, (6) Peering relationships are slightly locality-aware, and (7) Peer participation in simultaneous overlays follows a Zipf distribution. We believe that our findings can be used to understand current large-scale p2p streaming systems for future planning of resource usage, and to provide useful and practical hints for future design of large-scale p2p streaming systems.

Spectral methods for the detection of network community structure: a comparativeanalysis

Spectral analysis has been successfully applied to the detection of community structure ofnetworks, respectively being based on the adjacency matrix, the standard Laplacianmatrix, the normalized Laplacian matrix, the modularity matrix, the correlationmatrix and several other variants of these matrices. However, the comparisonbetween these spectral methods is less reported. More importantly, it is still unclearwhich matrix is more appropriate for the detection of community structure. Thispaper answers the question by evaluating the effectiveness of these five matricesagainst benchmark networks with heterogeneous distributions of node degree andcommunity size. Test results demonstrate that the normalized Laplacian matrix and thecorrelation matrix significantly outperform the other three matrices at identifyingthe community structure of networks. This indicates that it is crucial to takeinto account the heterogeneous distribution of node degree when using spectralanalysis for the detection of community structure. In addition, to our surprise, themodularity matrix exhibits very similar performance to the adjacency matrix,which indicates that the modularity matrix does not gain benefits from using theconfiguration model as a reference network with the consideration of the node degreeheterogeneity.