Principle Of Preferential Attachment Research Articles

Link prediction for long-circle-like networks.

Link prediction is the problem of predicting the uncertain relationship between a pair of nodes from observed structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observation of exemplars. Existing local and quasilocal link prediction algorithms with low computational complexity focus on regular complex networks with sufficiently many closed triangular motifs or on tree-like networks with the vast majority of open triangular motifs. However, the three-node motif cannot describe the local structural features of all networks, and we find the main structure of many networks is long line or closed circle that cannot be predicted well via traditional link prediction algorithms. Meanwhile, some global link prediction algorithms are effective but accompanied by high computational complexity. In this paper, we proposed a local method that is based on the natural characteristic of a long line-in contrast to the preferential attachment principle. Next, we test our algorithms for two kinds of symbolic long-circle-like networks: a metropolitan water distribution network and a sexual contact network. We find that our method is effective and performs much better than many traditional local and global algorithms. We adopt the community detection method to improve the accuracy of our algorithm, which shows that the long-circle-like networks also have clear community structure. We further suggest that the structural features are key for the link prediction problem. Finally, we propose a long-line network model to prove that our core idea is of universal significance.

Design and Analysis of Distributed Tree Growing Algorithms

Tree-based systems rely on real-time dissemination trees to deliver information to nodes. In order to offer good services, two fundamental aspects should guide the real-time growth process: low node degree and short distances to the server. In this paper, we propose a growth process to construct trees and make a detailed study on modeling and performance analysis of these tree-based systems. Our generative mechanism is based on the preferential attachment principle, where preference is given in terms of node quality. The proposed growth mechanism has a single parameter to weigh the relative importance of node degree and node distance on assessing node quality. We aim at understanding this mechanism when considering the local aspect of the node’s degree and the global aspect of the distance to a source. With this goal, we investigate our model through simulations and compare it to other growth processes. Our results indicate that the proposed model is capable of self-organizing nodes into good trees under six metrics of interest.

An investigation of network growth principles in the phonological language network.

This article investigated how network growth algorithms-preferential attachment, preferential acquisition, and lure of the associates-relate to the acquisition of words in the phonological language network, where edges are placed between words that are phonologically similar to each other. Through an archival analysis of age-of-acquisition norms from English and Dutch and word learning experiments, we examined how new words were added to the phonological network. Across both approaches, we found converging evidence that an inverse variant of preferential attachment-where new nodes were instead more likely to attach to existing nodes with few connections-influenced the growth of the phonological network. We suggest that the inverse preferential attachment principle reflects the constraints of adding new phonological representations to an existing language network with already many phonologically similar representations, possibly reflecting the pressures associated with the processing costs of retrieving lexical representations that have many phonologically similar competitors. These results contribute toward our understanding of how the phonological language network grows over time and could have implications for the learning outcomes of individuals with language disorders. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Epidemic spreading on evolving networks

Network structure will evolve over time, which will lead to changes in the spread of the epidemic. In this work, a network evolution model based on the principle of preferential attachment is proposed. The network will evolve into a scale-free network with a power-law exponent between 2 and 3 by our model, where the exponent is determined by the evolution parameters. We analyze the epidemic spreading process as the network evolves from a small-world one to a scale-free one, including the changes in epidemic threshold over time. The condition of epidemic threshold to increase is given with the evolution processes. The simulated results of real-world networks and synthetic networks show that as the network evolves at a low evolution rate, it is more conducive to preventing epidemic spreading.

Measuring network rewiring over time.

Recent years have seen tremendous advances in the scientific study of networks, as more and larger data sets of relationships among nodes have become available in many different fields. This has led to pathbreaking discoveries of near-universal network behavior over time, including the principle of preferential attachment and the emergence of scaling in complex networks. Missing from the set of network analysis methods to date is a measure that describes for each node how its relationship (or links) with other nodes changes from one period to the next. Conventional measures of network change for the most part show how the degrees of a node change; these are scalar comparisons. Our contribution is to use, for the first time, the cosine similarity to capture not just the change in degrees of a node but its relationship to other nodes. These are vector (or matrix)-based comparisons, rather than scalar, and we refer to them as “rewiring” coefficients. We apply this measure to three different networks over time to show the differences in the two types of measures. In general, bigger increases in our rewiring measure are associated with larger increases in network density, but this is not always the case.

Lyapunov–based Anomaly Detection in Preferential Attachment Networks

Abstract Network models aim to explain patterns of empirical relationships based on mechanisms that operate under various principles for establishing and removing links. The principle of preferential attachment forms a basis for the well-known Barabási–Albert model, which describes a stochastic preferential attachment process where newly added nodes tend to connect to the more highly connected ones. Previous work has shown that a wide class of such models are able to recreate power law degree distributions. This paper characterizes the cumulative degree distribution of the Barabási–Albert model as an invariant set and shows that this set is not only a global attractor, but it is also stable in the sense of Lyapunov. Stability in this context means that, for all initial configurations, the cumulative degree distributions of subsequent networks remain, for all time, close to the limit distribution. We use the stability properties of the distribution to design a semi-supervised technique for the problem of anomalous event detection on networks.

Die hedendaagse Afrikaanse poësiesisteem: Op soek na die mees verteenwoordigende wiskundige model van die rolspelerverhoudings daarbinne

Die sisteemteoretiese benadering tot die literatuurstudie is reeds deeglik gevestig, ook in Afrikaans. Sisteme kan as netwerke gemodelleer word en sedert die vyftigerjare van die vorige eeu is 'n groot aantal netwerkmodelle binne die wiskundige grafiekteorie ontwikkel. Die huidige studie vergelyk die hedendaagse Afrikaanse poësiesisteem en die Afrikaanse literêre sisteem van ander tydperke met twee netwerkmodelle ten einde te bepaal watter netwerkmodel die juisste voorstelling van Afrikaanse literêre netwerke verteenwoordig. Twee van die belangrikste netwerkmodelle in die wiskundige grafiekteorie, naamlik die lukrake netwerkmodel van Erdös en Rényi (1959; 1960 - voortaan die ER-model) en die skaalvrye netwerkmodel van Barabási en Albert (1999 - voortaan die BA-model), word bespreek en met behulp van Pearson se korrelasiekoëffisiënt word die korrelasies tussen die skakelverspreidingspatrone van Afrikaanse literêre netwerke en hierdie twee netwerkmodelle bereken. Daar word aangetoon dat sowel die hedendaagse Afrikaanse poësiesisteem as ander Afrikaanse literêre netwerke akkuraat met die BA-model gemodelleer kan word. Die betekenis van hierdie modellering word bespreek, veral met betrekking tot hoe die groei van die literêre netwerk daar uitsien, dit wil sê, deur Barabási se beginsel van selektiewe skakelvorming op die hedendaagse Afrikaanse poësie van toepassing te maak.

Constrained growth of complex scale-independent systems.

Scale independence is a ubiquitous feature of complex systems that implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution, and stock actions all feature scale independence. Assuming that they simply do, we focus here on describing how this behavior emerges, in contrast to more idealized models usually considered. We arrive at the conjecture that a minimal model to explain the growth toward scale independence involves only two coupled dynamical features: the first is the well-known preferential attachment principle, and the second is a general form of delayed temporal scaling. While the first is sufficient, the second is present in all studied data and appears to maximize the speed of convergence to true scale independence. The delay in this temporal scaling acts as a coupling between population growth and individual activity. Together, these two dynamical properties appear to pave a precise evolution path, such that even an instantaneous snapshot of a distribution is enough to reconstruct the past of the system and predict its future. We validate our approach and confirm its usefulness in diverse spheres of human activities, ranging from scientific and artistic productivity to sexual relations and online traffic.

Simulating adverse event spontaneous reporting systems as preferential attachment networks: application to the Vaccine Adverse Event Reporting System.

Spontaneous Reporting Systems [SRS] are critical tools in the post-licensure evaluation of medical product safety. Regulatory authorities use a variety of data mining techniques to detect potential safety signals in SRS databases. Assessing the performance of such signal detection procedures requires simulated SRS databases, but simulation strategies proposed to date each have limitations. We sought to develop a novel SRS simulation strategy based on plausible mechanisms for the growth of databases over time. We developed a simulation strategy based on the network principle of preferential attachment. We demonstrated how this strategy can be used to create simulations based on specific databases of interest, and provided an example of using such simulations to compare signal detection thresholds for a popular data mining algorithm. The preferential attachment simulations were generally structurally similar to our targeted SRS database, although they had fewer nodes of very high degree. The approach was able to generate signal-free SRS simulations, as well as mimicking specific known true signals. Explorations of different reporting thresholds for the FDA Vaccine Adverse Event Reporting System suggested that using proportional reporting ratio [PRR] > 3.0 may yield better signal detection operating characteristics than the more commonly used PRR > 2.0 threshold. The network analytic approach to SRS simulation based on the principle of preferential attachment provides an attractive framework for exploring the performance of safety signal detection algorithms. This approach is potentially more principled and versatile than existing simulation approaches. The utility of network-based SRS simulations needs to be further explored by evaluating other types of simulated signals with a broader range of data mining approaches, and comparing network-based simulations with other simulation strategies where applicable.

Microblog fans network evolving model based on user social characteristics and attractiveness of behavior properties

According to the research into how the users' social characteristics and behavior properties influence the microblog fans network evolving,a new microblog fans network evolving model based on the attractive factor called SBPAF was proposed.The attractive factor for social characteristics and the attractive factor for behavior properties were defined.The nodes create new edges according to attractive factor preferential attachment principle and the two-step attachment principle.Besides,the dying out of the edges was also considered.The parameter in the model can be adjusted flexibly so that different microblog fans networks can be simulated.Finally,the mathematical analysis and computational experiments verify that SBPAF model is reasonable and available.

A framework for modeling spatial node density in waypoint-based mobility

User mobility is of critical importance when designing mobile networks. In particular, "waypoint" mobility has been widely used as a simple way to describe how humans move. This paper introduces the first modeling framework to model waypoint-based mobility. The proposed framework is simple, yet general enough to model any waypoint-based mobility regimes. It employs first order ordinary differential equations to model the spatial density of participating nodes as a function of (1) the probability of moving between two locations within the geographic region under consideration, and (2) the rate at which nodes leave their current location. We validate our model against real user mobility recorded in GPS traces collected in three different scenarios. Moreover, we show that our modeling framework can be used to analyze the steady-state behavior of spatial node density resulting from a number of synthetic waypoint-based mobility regimes, including the widely used Random Waypoint model. Another contribution of the proposed framework is to show that using the well-known preferential attachment principle to model human mobility exhibits behavior similar to random mobility, where the original spatial node density distribution is not preserved. Finally, as an example application of our framework, we discuss using it to generate steady-state node density distributions to prime mobile network simulations.

On the formation of structure in growing networks

Based on the formation of triad junctions, the mechanism proposed in this paper generates networks that exhibit extended rather than single power law behavior. Triad formation guarantees strong neighborhood clustering and community-level characteristics as the network size grows to infinity. The asymptotic behavior is of interest in the study of directed networks in which (i) the formation of links cannot be described according to the principle of preferential attachment, (ii) the in-degree distribution fits a power law for nodes with a high degree and an exponential form otherwise, (iii) clustering properties emerge at multiple scales and depend on both the number of links that newly added nodes establish and the probability of forming triads, and (iv) groups of nodes form modules that feature fewer links to the rest of the nodes.

The Benefit of Imitating Particular Individuals

The Benefit of Imitating Particular Individuals

Is vocabulary growth influenced by the relations among words in a language learner’s vocabulary?

Several recent studies have explored the applicability of the preferential attachment principle to account for vocabulary growth. According to this principle, network growth can be described by a process in which existing nodes recruit new nodes with a probability that is an increasing function of their connectivity within the existing network. The current study combined subjective estimates of the age of acquisition (AoA) and associations among words in a large corpus to estimate the organization of semantic knowledge at multiple points in vocabulary growth. Consistent with previous studies, the number of connections or relations among words followed a power law distribution in which relatively few words were highly connected with other words and most words were connected to relatively few words. In addition, the growth in the number of connections of a word was a linear function of its initial number of connections, and the ratio of connections to any two words was relatively constant over time. Finally, number of connections to known words was a reliable predictor of a word's AoA. All of these findings can be shown to be consistent with the preferential attachment principle.

Heavy-tailed Distributions in Some Stochastic Dynamical Models

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the DegreeMass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavytailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics.

Chemical Basis of Metabolic Network Organization

Although the metabolic networks of the three domains of life consist of different constituents and metabolic pathways, they exhibit the same scale-free organization. This phenomenon has been hypothetically explained by preferential attachment principle that the new-recruited metabolites attach preferentially to those that are already well connected. However, since metabolites are usually small molecules and metabolic processes are basically chemical reactions, we speculate that the metabolic network organization may have a chemical basis. In this paper, chemoinformatic analyses on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG), Escherichia coli and Saccharomyces cerevisiae were performed. It was found that there exist qualitative and quantitative correlations between network topology and chemical properties of metabolites. The metabolites with larger degrees of connectivity (hubs) are of relatively stronger polarity. This suggests that metabolic networks are chemically organized to a certain extent, which was further elucidated in terms of high concentrations required by metabolic hubs to drive a variety of reactions. This finding not only provides a chemical explanation to the preferential attachment principle for metabolic network expansion, but also has important implications for metabolic network design and metabolite concentration prediction.

The Development of Social Media: Proposal for a Diffusion Model Incorporating Network Externalities in a Competitive Environment

The use of social media is highly concentrated. Since the appeal of this type of site lies in the richness of the content produced by the participants, this concentration phenomenon may be partly explained by network externalities. To demonstrate this effect in a competitive framework, the present study puts forward a diffusion model that incorporates the preferential attachment principle stemming from research on complex networks. The model is analyzed through a simulation applied to 51 social media in three different sectors. The results show that adding the attraction effect produced by the relative size of the network explains diffusion better than the classic Bass model.

Networks in biology: Handling biological complexity requires novel inputs into network theory

T he year 2009 was the tenth anniversary of the first publication on scale-free networks [1] and the fiftieth anniversary of the invention of random graphs [2]. Science magazine devoted a special section to review the present status of network theory, complexity research and its application to different disciplines [3]. Understanding and modeling complex systems without consideration of network topology and network evolution became out-of-date and practically impossible. The Erdos-Renyi model initiated a real break-through in the sense that statistical properties of graphs and networks became accessible without knowledge of the connection details. Among many other applications random networks became a useful reference in the biology of macromolecules for mapping polynucleotide sequences into structures [4]. Real world social networks, in particular communication networks, were found to have substantial shorter mean distances between agents than those predicted by the theory of random networks. Watts and Strogatz [5] invented networks that were found to match the available empirical data. These networks are called small-world networks as they have the small-world property [6], and they can be understood as intermediates between a regular lattice and a random graph. Watts and Strogatz characterize small-world networks by a degree of randomness (p), which varies between p 5 0 for the regular and p 5 1 for the random network. Only 1 year later, Barabasi and Albert conceived smallworld networks, which are created by the construction principle of preferential attachment [1]: Starting with a fully connected network of three nodes, further nodes are attached one by one with a larger probability for the incoming node to connect to a node that has already more neighbors. The resulting networks are scale-free—besides having the small-world property—and accordingly many of their properties fulfill power laws. Comparison with real world data from a great PETER SCHUSTER

PREFERENTIAL ATTACHMENT, AGING AND WEIGHTS IN RECOMMENDATION SYSTEMS

In the present work, algorithms based on complex network theory are applied to Recommendation Systems in order to improve their quality of predictions. We show how some networks are grown under the influence of trendy forces, and how this can be used to enhance the results of a recommendation system, i.e. increase their percentage of right predictions. After defining a base algorithm, we create recommendation networks which are based on a histogram of user ratings, using therefore an underlying principle of preferential attachment. We show the influence of data aging in the prediction of user habits and how the exact moment of the prediction influences the recommendation. Finally, we design weighted networks that take into account the age of the information used to generate the links. In this way, we obtain a better approximation to evaluate the users' tastes.

Network dynamics of eukaryotic LTR retroelements beyond phylogenetic trees

BackgroundSequencing projects have allowed diverse retroviruses and LTR retrotransposons from different eukaryotic organisms to be characterized. It is known that retroviruses and other retro-transcribing viruses evolve from LTR retrotransposons and that this whole system clusters into five families: Ty3/Gypsy, Retroviridae, Ty1/Copia, Bel/Pao and Caulimoviridae. Phylogenetic analyses usually show that these split into multiple distinct lineages but what is yet to be understood is how deep evolution occurred in this system.ResultsWe combined phylogenetic and graph analyses to investigate the history of LTR retroelements both as a tree and as a network. We used 268 non-redundant LTR retroelements, many of them introduced for the first time in this work, to elucidate all possible LTR retroelement phylogenetic patterns. These were superimposed over the tree of eukaryotes to investigate the dynamics of the system, at distinct evolutionary times. Next, we investigated phenotypic features such as duplication and variability of amino acid motifs, and several differences in genomic ORF organization. Using this information we characterized eight reticulate evolution markers to construct phenotypic network models.ConclusionThe evolutionary history of LTR retroelements can be traced as a time-evolving network that depends on phylogenetic patterns, epigenetic host-factors and phenotypic plasticity. The Ty1/Copia and the Ty3/Gypsy families represent the oldest patterns in this network that we found mimics eukaryotic macroevolution. The emergence of the Bel/Pao, Retroviridae and Caulimoviridae families in this network can be related with distinct inflations of the Ty3/Gypsy family, at distinct evolutionary times. This suggests that Ty3/Gypsy ancestors diversified much more than their Ty1/Copia counterparts, at distinct geological eras. Consistent with the principle of preferential attachment, the connectivities among phenotypic markers, taken as network-represented combinations, are power-law distributed. This evidences an inflationary mode of evolution where the system diversity; 1) expands continuously alternating vertical and gradual processes of phylogenetic divergence with episodes of modular, saltatory and reticulate evolution; 2) is governed by the intrinsic capability of distinct LTR retroelement host-communities to self-organize their phenotypes according to emergent laws characteristic of complex systems.ReviewersThis article was reviewed by Eugene V. Koonin, Eric Bapteste, and Enmanuelle Lerat (nominated by King Jordan)