Clustering Coefficient Distribution Research Articles

Optimization Algorithm of Communication Resource Allocation in a Complex Network Based on an Improved Neural Network

The traditional optimization algorithm of communication resource allocation in a complex network has the disadvantage of weak antijamming ability, and the communication quality decreases obviously when the number of users is large. In China’s large urban network applications, mobile phones and other networks can have problems such as reduced network efficiency when there are more access users at some communication base stations, thus affecting user network usage. An optimization algorithm of communication resource allocation in the complex network based on an improved neural network is proposed. Increase inertia improves the traditional BP neural network algorithm, using the average path length, clustering coefficient, and connectivity distribution index analysis of the complex network; the improved Hopfield neural network is utilized to confirm each user volume size; it is concluded that their users are able to get the number of subchannels, through the instantaneous channel coarse pair gain dynamic channel allocation, calculating bit load matrix at the same time, minimize transmission power, and achieve bit loading and power allocation and communication resource allocation optimization. Experimental results show that the proposed method has better application performance by introducing the improved neural network and suppressing the external interference on the basis of enhancing the communication effect.

A Network Sampling Strategy Inspired by Epidemic Spreading

Nowadays, network sampling has become an indispensable premise and foundation for large-scale network analysis, and its effectiveness determines to a large extent the reliability and practicability of the subsequent network analysis results. In this paper, we propose a network sampling algorithm inspired by an epidemic spreading model named the contact process. The contact process is similar to the random walk process but different from it in two key points. First, at each time step, a randomly selected sampled node rather than the latest sampled node is responsible for recruiting a new node from its neighborhood. Second, the responsible node recruits one of its neighbor nodes with a probability inversely proportional to the degree of this neighbor node, instead of equal probability. Experiments on nine indiscriminately selected real-world networks show that our proposed sampling algorithm has a significant advantage in preserving two basic network properties, the degree distributions and clustering coefficient distributions of original networks, compared with seven classical sampling methods.

Quantifying dissimilarities between heterogeneous networks with community structure

Quantifying dissimilarities between networks is a fundamental and challenging problem in network science. Current metrics for network comparison either assume the homogeneous distribution of nodal degrees or ignore the community structure of the network. Here we propose an efficient measure for comparing heterogeneous networks with communities from the perspective of probability distribution functions, which incorporates the nodal distance distribution, the clustering coefficient distribution and the alpha centrality distribution. Comparison between community benchmarks shows that the proposed measure returns non-zero values only when the networks are non-isomorphic.

THREE KEY PROPERTIES OF A SPECIAL CLASS OF EVOLVING NETWORKS BASED ON TOY-MODEL

In real world, many networks have self-similar structures at different length scales. In this paper, we propose a family of growing symmetrical networks based on toy-model from a deterministic initial graph. We aim to analyze its topological properties, such as the average path length, clustering coefficient and degree distribution, which uses iterative calculations and recursive methods.

A Network Theory Approach to Curriculum Design

In this paper we hypothesize that education, especially at the scale of curriculum, should be treated as a complex system composed of different ideas and concepts which are inherently connected. Therefore, the task of a good teacher lies in elucidating these connections and helping students make their own connections. Such a pedagogy allows students to personalize learning and strive to be ‘creative’ and make meaning out of old ideas. The novel contribution of this work lies in the mathematical approach we undertake to verify our hypothesis. We take the example of a precalculus course curriculum to make our case. We treat textbooks as exemplars of a specific pedagogy and map several texts into networks of isolated (nodes) and interconnected concepts (edges) thereby permitting computations of metrics which have much relevance to the education theorists, teachers and all others involved in the field of education. We contend that network metrics such as average path length, clustering coefficient and degree distribution provide valuable insights to teachers and students about the kind of pedagogy which encourages good teaching and learning.

Structural analysis of relevance propagation models

Relevance relations constitute the core of information retrieval. Topical ontologies, such as collaborative webpage classification projects, can provide a basis for identifying and analyzing such relations. New meaningful relevance relations can be automatically inferred from these ontologies by composing existing ones. In this work, several relevance propagation models are analyzed in terms of complex network theory. Structural properties such as Characteristic path length, Clustering coefficient and Degree distribution are computed over the models in order to understand the nature of each underlying network. This analysis raises interesting points about the Small-world and Scale-free structure of some relevance propagation models. Moreover, other connectivity and centrality measures are computed to gain additional insight into the topology of relevance. Finally, the analysis is complemented by providing visualizations of the k-core decomposition of different relevance propagation models. To illustrate the generalizability of the proposed methodology the analysis is carried out on an ontology from a different domain. The major theoretical implication of this analysis is the derivation of new instruments to typify semantic networks derived from relevance relations. The results can be exploited in a pragmatic way, as the parameters and properties derived by this analysis can serve as prior knowledge to algorithms for the automatic or semi-automatic construction of semantic networks.

A reduced model for complex network analysis of public transportation systems

Public transportation networks (PTNs) are represented as complex networks in order to analyze their robustness regarding node and link failures, to classify them into different theoretical network models, and to identify the characteristics of the underlying network. Usually, PTNs have a large amount of 1- and 2- degree nodes that blur the analysis and their characterization as complex networks. Subway and train-based transport networks present long single lines that connect central stations to far destinations differently from airport networks that usually have few large airports (hubs) connecting a significant number of small airports. By focusing on relevant network nodes and links and allowing comparisons between PTNs of different transportation modes, this paper proposes the Reduced Model as a simple method of network reduction that preserves the network skeleton (backbone structure) by properly removing 2-degree nodes of weighted and unweighted network representations. Different from other proposed methods, its simple formulation leads to mathematical expressions that show how the reduced model affects fundamental network metrics (degree, path length, and clustering coefficient distributions). The Reduced model is applied to four large real-world PTNs: (i) two Brazilian cities with bus-based transport; (ii) the Seoul metro network; (iii) a worldwide airport network. The results reveal a hub-based hierarchical structure when a large number of intermediary stops are present and small-world properties that emphasizes hub–hub connections after applying the Reduced model. Therefore, the reduced model emphasizes characteristics of the networks that could be difficult to identify without reduction.

Distance based amino acids network analysis

A study on different features of genetic codon analysis can provide us important insights on Amino Acids properties and protein evolution. The natural differentiation between the base positions in the codon, the chemical sorts of bases, purine, pyrimidine and their hydrogen bond number have been playing a pivotal role in the genetic code examination. Taking into consideration of these properties in this manuscript we have defined a distance measure among Amino Acids to study the evolutionary aspects of Amino Acids in protein synthesis. Later, we have applied a graph theoretic approach to study Amino Acids networks and analyzed its different centrality measures. We have also explored the correlation coefficient between centralities measure. Further, we have studied the clustering coefficient and degree distribution as different network parameters.

Generating Graphs by Creating Associative and Random Links Between Existing Nodes

The study and analysis of real-world social, communication, information and citation networks for understanding their structure and identifying interesting patterns have cultivated the need for designing generative models for such networks. A generative model generates an artificial but a realistic-looking network with the same characteristics as that of a real network under study. In this paper, we propose a new generative model for generating realistic networks. Our proposed model is a blend of three key ideas namely preferential attachment, associativity of social links and randomness in real networks. We present a framework that first tests these ideas separately and then blends them into a mixed model based on the idea that a real-world graph could be formed by a mixture of these concepts. Our model can be used for generating static as well as time evolving graphs and this feature distinguishes it from previous approaches. We compare our model with previous methods for generating graphs and show that it outperforms in several aspects. We compare our graphs with real-world graphs across many metrics such as degree, clustering coefficient and path length distributions, assortativity, eigenvector centrality and modularity. In addition, we give both qualitative and quantitative results for clarity.

Exploring small-world network with an elite-clique: Bringing embeddedness theory into the dynamic evolution of a venture capital network

This paper uses a network dynamics model to explain the formation of a small-world network with an elite-clique. This network is a small-world network with an elite-clique at its center in which elites are also the centers of many small groups. These leaders also act as bridges between different small groups. Network dynamics are an important research topic due to their ability to explain the evolution of network structures. In this paper, a Chinese Venture Capital (VC) network was coded from joint investments between VC firms and then analyzed to uncover its network properties and factors that influence its evolution. We first built a random graph model to control for factors such as network scale, network growth, investment frequency and syndication tendency. Then we added a partner-selection mechanism and used two theories to analyze the formation of network structure: relational embeddedness and structural embeddedness. After that, we ran simulations and compared the three models with the actual Chinese VC network. To do this we computed the elite-clique’s EI index, degree distribution, clustering coefficient distribution and motifs. Results show that adding embeddedness theories significantly improved the network dynamic model’s predictive power, and help us uncover the mechanisms that affect the formation of a small-world industrial network with an elite-clique at its center.

Nonlinear dynamics of river runoff elucidated by horizontal visibility graphs.

Horizontal Visibility Graphs (HVGs) are a recently developed method to construct networks from time series. The values of the time series are considered as the nodes of the network and are linked to each other if there is no larger value between them, such as they can "see" each other. The network properties reflect the nonlinear dynamics of the time series. For some classes of stochastic processes and for periodic time series, analytical results can be obtained for network-derived quantities such as the degree distribution, the local clustering coefficient distribution, the mean path length, and others. HVGs have the potential to discern between deterministic-chaotic and correlated-stochastic time series. Here, we investigate the sensitivity of the HVG methodology to properties and pre-processing of real-world data, i.e., time series length, the presence of ties, and deseasonalization, using a set of around 150 runoff time series from managed rivers at daily resolution from Brazil with an average length of 65 years. We show that an application of HVGs on real-world time series requires a careful consideration of data pre-processing steps and analysis methodology before robust results and interpretations can be obtained. For example, one recent analysis of the degree distribution of runoff records reported pronounced sub-exponential "long-tailed" behavior of North American rivers, whereas another study of South American rivers showed hyper-exponential "short-tailed" behavior resembling correlated noise. We demonstrate, using the dataset of Brazilian rivers, that these apparently contradictory results can be reconciled by minor differences in data-preprocessing (here: small differences in subtracting the seasonal cycle). Hence, data-preprocessing that is conventional in hydrology ("deseasonalization") changes long-term correlations and the overall runoff dynamics substantially, and we present empirical consequences and extensive simulations to investigate these issues from a HVG methodological perspective. After carefully accounting for these methodological aspects, the HVG analysis reveals that the river runoff dataset shows indeed complex behavior that appears to stem from a superposition of short-term correlated noise and "long-tailed behaviour," i.e., highly connected nodes. Moreover, the construction of a dam along a river tends to increase short-term correlations in runoff series. In summary, the present study illustrates the (often substantial) effects of methodological and data-preprocessing choices for the interpretation of river runoff dynamics in the HVG framework and its general applicability for real-world time series.

Nonredundant, Highly Connected MicroRNAs Control Functionality in Breast Cancer Networks.

Alterations to transcriptional regulation are an important factor in breast cancer. Noncoding RNA, such as microRNA (miR), have very influential roles in the transcriptional regulation of genes. Transcriptional regulation can be successfully modeled and analyzed using complex network theory. Particularly, interactions between two distinct classes of biological elements, such as miR and genes, can be approached through the bipartite network formalism. Based on bipartite network properties, it is possible to identify highly influential miRs in the network, such as those that have a large number of connections indicating regulation of a large set of genes. Some miRs in a network are nonredundant, which indicates that they are solely responsible of the regulation of a particular set of genes, which in turn may be associated to a particular biological process. We hypothesize that highly influential, nonredundant miRs, which we call Commodore miRs (Cdre-miRs), have an important role on the control of biological functions through transcriptional networks. In this work, we analyze the regulation of gene expression by miRs in healthy and cancerous breast tissue using bipartite miR-gene networks inferred from the Cancer Genome Atlas (TCGA) expression data. We observe differences in the degree, clustering coefficient and redundancy distributions for miRs and genes in the network, indicating differences in the way that these elements interact with each other. Furthermore, we identify a small set of five Cdre-miRs in the breast cancer network: miR-190b, miR-let7i, miR-292-b, miR-511, and miR-141. The neighborhood of genes controlled by each of these miRs is involved in particular biological functions such as dynein structure-associated processes, immune response, angiogenesis, cytokine activity, and cell motility. We propose that these Cdre-miRs are important control elements of biological functions deregulated in breast cancer.

Network analysis of the COSMOS galaxy field

The galaxy data provided by COSMOS survey for 1 by 1 degree field of sky are analysed by methods of complex networks. Three galaxy samples (slices) with redshifts ranging within intervals 0.88-0.91, 0.91-0.94 and 0.94-0.97 are studied as two-dimensional projections for the spatial distributions of galaxies. We construct networks and calculate network measures for each sample, in order to analyse the network similarity of different samples, distinguish various topological environments, and find associations between galaxy properties (colour index and stellar mass) and their topological environments. Results indicate a high level of similarity between geometry and topology for different galaxy samples and no clear evidence of evolutionary trends in network measures. The distribution of local clustering coefficient C manifests three modes which allow for discrimination between stand-alone singlets and dumbbells (0 <= C <= 0.1), intermediately (0 < C < 0.9) and clique (0.9 <= C <= 1) like galaxies. Analysing astrophysical properties of galaxies (colour index and stellar masses), we show that distributions are similar in all slices, however weak evolutionary trends can also be seen across redshift slices. To specify different topological environments we have extracted selections of galaxies from each sample according to different modes of C distribution. We have found statistically significant associations between evolutionary parameters of galaxies and selections of C: the distribution of stellar mass for galaxies with interim C differ from the corresponding distributions for stand-alone and clique galaxies, and this difference holds for all redshift slices. The colour index realises somewhat different behaviour.

Топология сети межбанковского кредитования в агентной модели банковской системы

The study analyzes the topology of the interbank network in the agent-based model of the banking system with detailed description of the protocols and stylized one of the external (with respect to the banking system) economy. It is shown that the main incentive for the inter­bank market creation originates from liquidity gaps resulting from maturities mismatch bet­ween deposits and credits. The impact of this effect on the dynamics of total capital and cash in the case of increasing term structure of the yield curve generating credit and deposit’s maturities mismatch as a result of banks optimizing behavior, is illustrated. Different properties of this graph are compared to those of the real interbank networks. It is shown that the model in which banks are represented by agents-automata can reproduce various topological properties of the real interbank networks. These properties are: significant size of the giant strongly connected component, fat‑tailed nature of the distributions of In- and Out-degrees, fat-tailed nature of the distribution of allocated funds, disassortativity, nonuniformity of the distribution of clustering coefficient over the vertices. The properties which can be reproduced only in the model with a more detailed description of agents’ behavior were also marked out. These properties are the following: absence of the oriented cycles in the networks with low aggregation of the data, low fraction of the banks not participating in the interbank market and of the net-creditor banks, absence of fat tails in the distribution over the borrowed funds, low clustering coefficient. The reasons for such a difference between the properties of model networks and the real ones are noted. The changes of the model needed to reproduce such properties of real networks are discussed.

Spatial connections in regional climate model rainfall outputs at different temporal scales: Application of network theory

Understanding the spatial and temporal variability of rainfall has always been a great challenge, and the impacts of climate change further complicate this issue. The present study employs the concepts of complex networks to study the spatial connections in rainfall, with emphasis on climate change and rainfall scaling. Rainfall outputs (during 1961–1990) from a regional climate model (i.e. Weather Research and Forecasting (WRF) model that downscaled the European Centre for Medium-range Weather Forecasts, ECMWF ERA-40 reanalyses) over Southeast Asia are studied, and data corresponding to eight different temporal scales (6-hr, 12-hr, daily, 2-day, 4-day, weekly, biweekly, and monthly) are analyzed. Two network-based methods are applied to examine the connections in rainfall: clustering coefficient (a measure of the network’s local density) and degree distribution (a measure of the network’s spread). The influence of rainfall correlation threshold (T) on spatial connections is also investigated by considering seven different threshold levels (ranging from 0.5 to 0.8). The results indicate that: (1) rainfall networks corresponding to much coarser temporal scales exhibit properties similar to that of small-world networks, regardless of the threshold; (2) rainfall networks corresponding to much finer temporal scales may be classified as either small-world networks or scale-free networks, depending upon the threshold; and (3) rainfall spatial connections exhibit a transition phase at intermediate temporal scales, especially at high thresholds. These results suggest that the most appropriate model for studying spatial connections may often be different at different temporal scales, and that a combination of small-world and scale-free network models might be more appropriate for rainfall upscaling/downscaling across all scales, in the strict sense of scale-invariance. The results also suggest that spatial connections in the studied rainfall networks in Southeast Asia are weak, especially when more stringent conditions are imposed (i.e. when T is very high), except at the monthly scale.

Functional architecture and global properties of the Corynebacterium glutamicum regulatory network: Novel insights from a dataset with a high genomic coverage

Corynebacterium glutamicum is a Gram-positive, anaerobic, rod-shaped soil bacterium able to grow on a diversity of carbon sources like sugars and organic acids. It is a biotechnological relevant organism because of its highly efficient ability to biosynthesize amino acids, such as l-glutamic acid and l-lysine. Here, we reconstructed the most complete C. glutamicum regulatory network to date and comprehensively analyzed its global organizational properties, systems-level features and functional architecture. Our analyses show the tremendous power of Abasy Atlas to study the functional organization of regulatory networks. We created two models of the C. glutamicum regulatory network: all-evidences (containing both weak and strong supported interactions, genomic coverage=73%) and strongly-supported (only accounting for strongly supported evidences, genomic coverage=71%). Using state-of-the-art methodologies, we prove that power-law behaviors truly govern the connectivity and clustering coefficient distributions. We found a non-previously reported circuit motif that we named complex feed-forward motif. We highlighted the importance of feedback loops for the functional architecture, beyond whether they are statistically over-represented or not in the network. We show that the previously reported top-down approach is inadequate to infer the hierarchy governing a regulatory network because feedback bridges different hierarchical layers, and the top-down approach disregards the presence of intermodular genes shaping the integration layer. Our findings all together further support a diamond-shaped, three-layered hierarchy exhibiting some feedback between processing and coordination layers, which is shaped by four classes of systems-level elements: global regulators, locally autonomous modules, basal machinery and intermodular genes.

Deterministic hierarchical networks

It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems.

Complex quantum network geometries: Evolution and phase transitions.

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Are feedback loops destructive to synchronization?

We study the effects of directionality on synchronization of dynamical networks. Performing the linear stability analysis and the numerical simulation of the Kuramoto model in directed networks, we show that balancing in- and out-degrees of all nodes enhances the synchronization of sparse networks, especially in networks with high clustering coefficient and homogeneous degree distribution. Furthermore, by omitting all the feedback loops, we show that while hierarchical directed acyclic graphs are structurally highly synchronizable, their global synchronization is too sensitive to the choice of natural frequencies and is strongly affected by noise.

Complex networks from space-filling bearings.

Two-dimensional space-filling bearings are dense packings of disks that can rotate without slip. We consider the entire first family of bearings for loops of four disks and propose a hierarchical construction of their contact network. We provide analytic expressions for the clustering coefficient and degree distribution, revealing bipartite scale-free behavior with a tunable degree exponent depending on the bearing parameters. We also analyze their average shortest path and percolation properties.