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Phonological networks are representations of word forms and their phonological relationships with other words in a given language lexicon. A principle underlying the growth (or evolution) of those networks is preferential attachment, or the "rich-gets-richer" mechanisms, according to which words with many phonological neighbors (or links) are the main beneficiaries of future growth opportunities. Due to their limited number of words, language lexica constitute node-constrained networks where growth cannot keep increasing in a linear way; hence, preferential attachment is likely mitigated by certain factors. The present study investigated obsolescence effects (i.e., a word's finite timespan of being active in terms of growth) in an evolving phonological network of English as a second language. It was found that phonological neighborhoods are constructed by one large initial lexical spurt, followed by sublinear growth spurts that eventually lead to very limited growth in later lexical spurts during network evolution. First-language-given neighborhood densities are rarely reached even by the most advanced language learners. An analysis of the strength of phonological relationships between phonological word forms revealed a tendency to incorporate phonetically more distant phonological neighbors at earlier acquisition stages. Overall, the findings suggest an obsolescence effect in growth that favors younger words. Implications for the second-language lexicon include leveraged learning mechanisms and learning bouts focused on a smaller range of phonological segments, and involve questions concerning lexical processing in aging networks., (© 2023. The Author(s).)

We study potential biases of popular network clustering quality metrics, such as those based on the dichotomy between internal and external connectivity. We propose a method that uses both stochastic and preferential attachment block models construction to generate networks with preset community structures, and Poisson or scale-free degree distribution, to which quality metrics will be applied. These models also allow us to generate multi-level structures of varying strength, which will show if metrics favour partitions into a larger or smaller number of clusters. Additionally, we propose another quality metric, the density ratio. We observed that most of the studied metrics tend to favour partitions into a smaller number of big clusters, even when their relative internal and external connectivity are the same. The metrics found to be less biased are modularity and density ratio., Competing Interests: The authors declare that they have no competing interests., (© 2023 Renedo-Mirambell and Arratia.)

Private businesses are often entrusted with public contracts, wherein public money is allocated to a private company. This process raises concerns about transparency, even in the most developed democracies. But are there any regularities guiding this process? Do all private companies benefit equally from the state budgets? Here, we tackle these questions focusing on the case of Slovenia, which keeps excellent records of this kind of public spending. We examine a dataset detailing every transfer of public money to the private sector from January 2003 to May 2020. During this time, Slovenia has conducted business with no less than 248 989 private companies. We find that the cumulative distribution of money received per company can be reasonably well explained by a power-law or lognormal fit. We also show evidence for the first-mover advantage, and determine that companies receive new funding in a way that is roughly linear over time. These results indicate that, despite all human factors involved, Slovenian public spending is at least to some extent regulated by emergent self-organizing principles., Competing Interests: We declare we have no competing interests., (© 2023 The Authors.)

Studies on policy change focus on governmental decision-making from a technical rationality perspective, ignoring the fact that policy change is a complicated social construction process involving multiple actors. This study used the modified advocacy coalition framework to explain changes in China's family planning policy and discourse network analysis to show the debate on the birth control policy among multiple actors (central government, local governments, experts, media, and the public). It found that the dominant coalition and the minority coalition can learn and adjust deep core beliefs from each other; the sharing and flow of actors' policy beliefs drive change in the network structure; and actors' obvious preferential attachment when the promulgation of the central document, are all helpful in policy change. This study can explain macro-policy changes from a micro-perspective to reveal the process and mechanism of policy changes in China's authoritarian regime., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Preferential attachment (PA) is a widely observed behavior in many living systems and has been used in modeling many networks. The aim of this work is to show that the mechanism of PA is a consequence of the fundamental principle of least effort. We derive PA directly from this principle in maximizing an efficiency function. This approach not only allows a better understanding of the different PA mechanisms already reported but also naturally extends these mechanisms with a non-power law probability of attachment. The possibility of using the efficiency function as a general measure of attachment efficiency is also investigated.

Consensus about the universality of the power law feature in complex networks is experiencing widespread challenges. In this paper, we propose a generic theoretical framework in order to examine the power law property. First, we study a class of birth-and-death networks that are more common than BA networks in the real world, and then we calculate their degree distributions; the results show that the tails of their degree distributions exhibit a distinct power law feature. Second, we suggest that in the real world two important factors-network size and node disappearance probability-will affect the analysis of power law characteristics in observation networks. Finally, we suggest that an effective way of detecting the power law property is to observe the asymptotic (limiting) behavior of the degree distribution within its effective intervals.

In this paper, we use the methods of networks science to analyse the transaction networks of tokens running on the Ethereum blockchain. We start with a deep dive on four of them: Ampleforth (AMP), Basic Attention Token (BAT), Dai (DAI) and Uniswap (UNI). We study two types of blockchain addresses, smart contracts (SC), which run code, and externally owned accounts (EOA), run by human users, or off-chain code, with the corresponding private keys. We use preferential attachment and network dismantling strategies to evaluate their importance for the network structure. Subsequently, we expand our view to all ERC-20 tokens issued on the Ethereum network. We first study multilayered networks composed of Ether (ETH) and individual tokens using a dismantling approach to assess how the deconstruction starting from one network affects the other. Finally, we analyse the Ether network and Ethereum-based token networks to find similarities between sets of high-degree nodes. For this purpose, we use both the traditional Jaccard Index and a new metric that we introduce, the Ordered Jaccard Index (OJI), which considers the order of the elements in the two sets that are compared. Our findings suggest that smart contracts and exchange-related addresses play a structural role in transaction networks both in DeFi and Ethereum. The presence in the network of nodes associated to addresses of smart contracts and exchanges is positively correlated with the success of the token network measured in terms of network size and market capitalisation. These nodes play a fundamental role in the centralisation of the supposedly decentralised finance (DeFi) ecosystem: without them, their networks would quickly collapse.

Muscle atrophy is a side effect of several terrestrial diseases which also affects astronauts severely in space missions due to the reduced gravity in spaceflight. An integrative graph-theoretic network-based drug repurposing methodology quantifying the interplay of key gene regulations and protein-protein interactions in muscle atrophy conditions is presented. Transcriptomic datasets from mice in spaceflight from GeneLab have been extensively mined to extract the key genes that cause muscle atrophy in organ muscle tissues such as the thymus, liver, and spleen. Top muscle atrophy gene regulators are selected by Bayesian Markov blanket method and gene-disease knowledge graph is constructed using the scalable precision medicine knowledge engine. A deep graph neural network is trained for predicting links in the network. The top ranked diseases are identified and drugs are selected for repurposing using drug bank resource. A disease drug knowledge graph is constructed and the graph neural network is trained for predicting new drugs. The results are compared with machine learning methods such as random forest, and gradient boosting classifiers. Network measure based methods shows that preferential attachment has good performance for link prediction in both the gene-disease and disease-drug graphs. The receiver operating characteristic curves, and prediction accuracies for each method show that the random walk similarity measure and deep graph neural network outperforms the other methods. Several key target genes identified by the graph neural network are associated with diseases such as cancer, diabetes, and neural disorders. The novel link prediction approach applied to the disease drug knowledge graph identifies the Monoclonal Antibodies drug therapy as suitable candidate for drug repurposing for spaceflight induced microgravity. There are a total of 21 drugs identified as possible candidates for treating muscle atrophy. Graph neural network is a promising deep learning architecture for link prediction from gene-disease, and disease-drug networks., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Manian, Orozco-Sandoval and Diaz-Martinez.)

We develop an early warning system and subsequent optimal intervention policy to avoid the formation of disproportional dominance ("winner takes all," WTA) in growing complex networks. This is modeled as a system of interacting agents, whereby the rate at which an agent establishes connections to others is proportional to its already existing number of connections and its intrinsic fitness. We derive an exact four-dimensional phase diagram that separates the growing system into two regimes: one where the "fit get richer" and one where, eventually, the WTA. By calibrating the system's parameters with maximum likelihood, its distance from the unfavorable WTA regime can be monitored in real time. This is demonstrated by applying the theory to the eToro social trading platform where users mimic each other's trades. If the system state is within or close to the WTA regime, we show how to efficiently control the system back into a more stable state along a geodesic path in the space of fitness distributions. It turns out that the common measure of penalizing the most dominant agents does not solve sustainably the problem of drastic inequity. Instead, interventions that first create a critical mass of high-fitness individuals followed by pushing the relatively low-fitness individuals upward is the best way to avoid swelling inequity and escalating fragility., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)

Here, we view the mental lexicon as a semantic network where words are connected if they are semantically related. Steyvers and Tenenbaum (Cognitive Science, 29, 41-78, 2005) proposed that the growth of semantic networks follows preferential attachment, the observation that new nodes are more likely to connect to preexisting nodes that are more well connected (i.e., the rich get richer). If this is the case, well-connected known words should be better at acquiring new links than poorly connected words. We tested this prediction in three paired-associate learning (PAL) experiments in which participants memorized arbitrary cue-response word pairs. We manipulated the semantic connectivity of the cue words, indexed by the words' free associative degree centrality. Experiment 1 is a reanalysis of the PAL data from Qiu and Johns (Psychonomic Bulletin & Review, 27, 114-121, 2020), in which young adults remembered 40 cue-response word pairs (e.g., nature-chain) and completed a cued recall task. Experiment 2 is a preregistered replication of Qiu and Johns. Experiment 3 addressed some limitations in Qiu and Johns's design by using pseudowords as the response items (e.g., boot-arruity). The three experiments converged to show that cue words of higher degree centrality facilitated the recall/recognition of the response items, providing support for the notion that better-connected words have a greater ability to acquire new links (i.e., the rich do get richer). Importantly, while degree centrality consistently accounted for significant portions of variance in PAL accuracy, other psycholinguistic variables (e.g., concreteness, contextual diversity) did not, suggesting that degree centrality is a distinct variable that affects the ease of verbal associative learning.

Recent work investigating the development of the phonological lexicon, where edges between words represent phonological similarity, have suggested that phonological network growth may be partly driven by a process that favors the acquisition of new words that are phonologically similar to several existing words in the lexicon. To explore this growth mechanism, we conducted a simulation study to examine the properties of networks grown by inverse preferential attachment, where new nodes added to the network tend to connect to existing nodes with fewer edges. Specifically, we analyzed the network structure and degree distributions of artificial networks generated via either preferential attachment, an inverse variant of preferential attachment, or combinations of both network growth mechanisms. The simulations showed that network growth initially driven by preferential attachment followed by inverse preferential attachment led to densely-connected network structures (i.e., smaller diameters and average shortest path lengths), as well as degree distributions that could be characterized by non-power law distributions, analogous to the features of real-world phonological networks. These results provide converging evidence that inverse preferential attachment may play a role in the development of the phonological lexicon and reflect processing costs associated with a mature lexicon structure.

We propose a new citation model which builds on the existing models that explicitly or implicitly include "direct" and "indirect" (learning about a cited paper's existence from references in another paper) citation mechanisms. Our model departs from the usual, unrealistic assumption of uniform probability of direct citation, in which initial differences in citation arise purely randomly. Instead, we demonstrate that a two-mechanism model in which the probability of direct citation is proportional to the number of authors on a paper (team size) is able to reproduce the empirical citation distributions of articles published in the field of astronomy remarkably well, and at different points in time. Interpretation of our model is that the intrinsic citation capacity, and hence the initial visibility of a paper, will be enhanced when more people are intimately familiar with some work, favoring papers from larger teams. While the intrinsic citation capacity cannot depend only on the team size, our model demonstrates that it must be to some degree correlated with it, and distributed in a similar way, i.e., having a power-law tail. Consequently, our team-size model qualitatively explains the existence of a correlation between the number of citations and the number of authors on a paper.

The development of online social networking services provides a rich source of data of social networks including geospatial information. More and more research has shown that geographical space is an important factor in the interactions of users in social networks. In this paper, we construct the spatial interaction network from the city level, which is called the city interaction network, and study the evolution mechanism of the city interaction network formed in the process of information dissemination in social networks. A network evolution model for interactions among cities is established. The evolution model consists of two core processes: the edge arrival and the preferential attachment of the edge. The edge arrival model arranges the arrival time of each edge; the model of preferential attachment of the edge determines the source node and the target node of each arriving edge. Six preferential attachment models (Random-Random, Random-Degree, Degree-Random, Geographical distance, Degree-Degree, Degree-Degree-Geographical distance) are built, and the maximum likelihood approach is used to do the comparison. We find that the degree of the node and the geographic distance of the edge are the key factors affecting the evolution of the city interaction network. Finally, the evolution experiments using the optimal model DDG are conducted, and the experiment results are compared with the real city interaction network extracted from the information dissemination data of the WeChat web page. The results indicate that the model can not only capture the attributes of the real city interaction network, but also reflect the actual characteristics of the interactions among cities.

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási-Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics., Competing Interests: The author declares no conflict of interest.

The processes whereby ecological networks emerge, persist and decay throughout ecosystem development are largely unknown. Here we study networks of plant and arbuscular mycorrhizal fungal (AMF) communities along a 120 000 year soil chronosequence, as they undergo assembly (progression) and then disassembly (retrogression). We found that network assembly and disassembly were symmetrical, self-reinforcing processes that together were capable of generating key attributes of network architecture. Plant and AMF species that had short indirect paths to others in the community (i.e. high centrality), rather than many direct interaction partners (i.e. high degree), were best able to attract new interaction partners and, in the case of AMF species, also to retain existing interactions with plants during retrogression. We then show using simulations that these non-random patterns of attachment and detachment promote nestedness of the network. These results have implications for predicting extinction sequences, identifying focal points for invasions and suggesting trajectories for restoration., (© 2018 John Wiley & Sons Ltd/CNRS.)

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli random graph, in which any two nodes have the same probability of being connected, does. Therefore, to study the propagation of "infection" across a social network, we propose a network epidemic model by combining a stochastic epidemic model and a preferential attachment model. A simulation study based on the subsequent Markov Chain Monte Carlo algorithm reveals an identifiability issue with the model parameters. Finally, the network epidemic model is applied to a set of online commissioning data., (© The Author(s) 2017.)

Numerous studies have investigated the remarkable variation of social features and the resulting structures across species. Indeed, relationships are dynamic and vary in time according to various factors such as environmental conditions or individuals attributes. However, few studies have investigated the processes that stabilize the structures within a given species, and the behavioral mechanisms that ensure their coherence and continuity across time. Here, we used a dynamic actor-based model, RSiena, to investigate the consistency of the temporal dynamic of relationships of a group of captive rooks facing recurrent modifications in group composition (i.e., the loss and introduction of individuals). We found that changes in relationships (i.e., formation and removal) followed consistent patterns regardless of group composition and sex-ratio. Rooks preferentially interacted with paired congeners (i.e., unpopular attachment) and were more likely to form relationships with individuals bonded to a current social partner (i.e., "friends of friends", or triadic closure). The sex of individuals had no effect on the dynamic of relationships. This robust behavioral mechanisms formed the basis of inter-connected networks, composed of sub-structures of individuals emerging from the enmeshment of dyadic and triadic motifs. Overall, the present study reveals crucial aspects of the behavioral mechanisms shaping rooks social structure, suggesting that rooks live in a well-integrated society, going far beyond the unique monogamous pair-bond.

This study applied a temporal social network analysis model to describe three affiliative social networks (allogrooming, sleep in contact, and triadic interaction) in a non-human primate species, Macaca sylvanus. Three main social mechanisms were examined to determine interactional patterns among group members, namely preferential attachment (i.e., highly connected individuals are more likely to form new connections), triadic closure (new connections occur via previous close connections), and homophily (individuals interact preferably with others with similar attributes). Preferential attachment was only observed for triadic interaction network. Triadic closure was significant in allogrooming and triadic interaction networks. Finally, gender homophily was seasonal for allogrooming and sleep in contact networks, and observed in each period for triadic interaction network. These individual-based behaviors are based on individual reactions, and their analysis can shed light on the formation of the affiliative networks determining ultimate coalition networks, and how these networks may evolve over time. A focus on individual behaviors is necessary for a global interactional approach to understanding social behavior rules and strategies. When combined, these social processes could make animal social networks more resilient, thus enabling them to face drastic environmental changes. This is the first study to pinpoint some of the processes underlying the formation of a social structure in a non-human primate species, and identify common mechanisms with humans. The approach used in this study provides an ideal tool for further research seeking to answer long-standing questions about social network dynamics., (© 2017 Wiley Periodicals, Inc.)

During decades the study of networks has been divided between the efforts of social scientists and natural scientists, two groups of scholars who often do not see eye to eye. In this review I present an effort to mutually translate the work conducted by scholars from both of these academic fronts hoping to continue to unify what has become a diverging body of literature. I argue that social and natural scientists fail to see eye to eye because they have diverging academic goals. Social scientists focus on explaining how context specific social and economic mechanisms drive the structure of networks and on how networks shape social and economic outcomes. By contrast, natural scientists focus primarily on modeling network characteristics that are independent of context, since their focus is to identify universal characteristics of systems instead of context specific mechanisms. In the following pages I discuss the differences between both of these literatures by summarizing the parallel theories advanced to explain link formation and the applications used by scholars in each field to justify their approach to network science. I conclude by providing an outlook on how these literatures can be further unified.

This paper examines the collaboration structures and dynamics of the co-authorship network of all Slovenian researchers. Its goal is to identify the key factors driving collaboration and the main differences in collaboration behavior across scientific fields and disciplines. Two approaches to modelling network dynamics are combined in this paper: the small-world model and the mechanism of preferential attachment, also known as the process of cumulative advantage. Stochastic-actor-based modelling of co-authorship network dynamics uses data for the complete longitudinal co-authorship networks for the entire Slovenian scientific community from 1996 to 2010. We confirmed the presence of clustering in all fields and disciplines. Preferential attachment is far more complex than a single global mechanism. There were two clear distinctions regarding collaboration within scientific fields and disciplines. One was that some fields had an internal national saturation inhibiting further collaboration. The second concerned the differential impact of collaboration with scientists from abroad on domestic collaboration. In the natural, technical, medical, and biotechnical sciences, this promotes collaboration within the Slovenian scientific community while in the social sciences and humanities this inhibits internal collaboration.

The Matthew effect describes the phenomenon that in societies, the rich tend to get richer and the potent even more powerful. It is closely related to the concept of preferential attachment in network science, where the more connected nodes are destined to acquire many more links in the future than the auxiliary nodes. Cumulative advantage and success-breads-success also both describe the fact that advantage tends to beget further advantage. The concept is behind the many power laws and scaling behaviour in empirical data, and it is at the heart of self-organization across social and natural sciences. Here, we review the methodology for measuring preferential attachment in empirical data, as well as the observations of the Matthew effect in patterns of scientific collaboration, socio-technical and biological networks, the propagation of citations, the emergence of scientific progress and impact, career longevity, the evolution of common English words and phrases, as well as in education and brain development. We also discuss whether the Matthew effect is due to chance or optimization, for example related to homophily in social systems or efficacy in technological systems, and we outline possible directions for future research.

Seemingly similar individuals often experience drastically different success trajectories, with some repeatedly failing and others consistently succeeding. One explanation is preexisting variability along unobserved fitness dimensions that is revealed gradually through differential achievement. Alternatively, positive feedback operating on arbitrary initial advantages may increasingly set apart winners from losers, producing runaway inequality. To identify social feedback in human reward systems, we conducted randomized experiments by intervening in live social environments across the domains of funding, status, endorsement, and reputation. In each system we consistently found that early success bestowed upon arbitrarily selected recipients produced significant improvements in subsequent rates of success compared with the control group of nonrecipients. However, success exhibited decreasing marginal returns, with larger initial advantages failing to produce much further differentiation. These findings suggest a lesser degree of vulnerability of reward systems to incidental or fabricated advantages and a more modest role for cumulative advantage in the explanation of social inequality than previously thought.

Network Growth Models such as Preferential Attachment and Duplication/Divergence are popular generative models with which to study complex networks in biology, sociology, and computer science. However, analyzing them within the framework of model selection and statistical inference is often complicated and computationally difficult, particularly when comparing models that are not directly related or nested. In practice, ad hoc methods are often used with uncertain results. If possible, the use of standard likelihood-based statistical model selection techniques is desirable. With this in mind, we develop an Adaptive Importance Sampling algorithm for estimating likelihoods of Network Growth Models. We introduce the use of the classic Plackett-Luce model of rankings as a family of importance distributions. Updates to importance distributions are performed iteratively via the Cross-Entropy Method with an additional correction for degeneracy/over-fitting inspired by the Minimum Description Length principle. This correction can be applied to other estimation problems using the Cross-Entropy method for integration/approximate counting, and it provides an interpretation of Adaptive Importance Sampling as iterative model selection. Empirical results for the Preferential Attachment model are given, along with a comparison to an alternative established technique, Annealed Importance Sampling.