Network growth models: A behavioural basis for attachment proportional to fitness

Clique densification in networks

Real-world networks are rarely static. Recently, there has been increasing interest in both network growth and network densification, in which the number of edges scales superlinearly with the number of nodes. Less studied but equally important, however, are scaling laws of higher-order cliques, which can drive clustering and network redundancy. In this paper, we study how cliques grow with network size, by analyzing several empirical networks from emails to Wikipedia interactions. Our results show superlinear scaling laws whose exponents increase with clique size, in contrast to predictions from a previous model. We then show that these results are in qualitative agreement with a model that we propose, the local preferential attachment model, where an incoming node links not only to a target node, but also to its higher-degree neighbors. Our results provide insights into how networks grow and where network redundancy occurs.

Graphlet correlation distance to compare small graphs

Graph models are standard for representing mutual relationships between sets of entities. Often, graphs deal with a large number of entities with a small number of connections (e.g. social media relationships, infectious disease spread). The distances or similarities between such large graphs are known to be well established by the Graphlet Correlation Distance (GCD). This paper deals with small graphs (with potentially high densities of connections) that have been somewhat neglected in the literature but that concern important fora like sociology, ecology and fisheries, to mention some examples. First, based on numerical experiments, we study the conditions under which Erdős-Rényi, Fitness Scale-Free, Watts-Strogatz small-world and geometric graphs can be distinguished by a specific GCD measure based on 11 orbits, the GCD11. This is done with respect to the density and the order (i.e. the number of nodes) of the graphs when comparing graphs with the same and different orders. Second, we develop a randomization statistical test based on the GCD11 to compare empirical graphs to the four possible null models used in this analysis and apply it to a fishing case study where graphs represent pairwise proximity between fishing vessels. The statistical test rules out independent pairing within the fleet studied which is a standard assumption in fisheries. It also illustrates the difficulty to identify similarities between real-world small graphs and graph models.

Analysis of network disruption evolution of Chinese fresh cold chain under COVID-19

The spread of the global COVID-19 epidemic, home quarantine, and blockade of infected areas are essential measures to prevent the spread of the epidemic, but efforts to prevent and control the outbreak lead to the disruption of fresh and cold chain agricultural products in the region. Based on the multi-layer management model of non-scale agricultural households in China, we applied the complex network theory to construct an evolutionary model of the Chinese fresh cold chain network with adaptation degree priority connection, dual local world considering transport distance connection relationship, and superiority and inferiority mechanism. Based on this model, we studied the evolution of fresh cold chain disruption, and puts forward the optimal design of fresh cold chain network disruption and reconnection from the perspective of practicality and economy.

Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model

Monkeypox (MPX) is a viral zoonotic disease that was endemic to Central and West Africa. However, during the first half of 2022, MPX spread to almost 60 countries all over the world. Smallpox vaccines are about 85% effective in preventing MPX infections. Our objective is to determine whether the vaccines should be mandated or whether voluntary use of the vaccine could be enough to stop the MPX outbreak. We incorporate a standard SVEIR compartmental model of MPX transmission into a game-theoretical framework. We study a vaccination game in which individuals decide whether or not to vaccinate by assessing their benefits and costs. We solve the game for Nash equilibria, i.e., the vaccination rates the individuals would likely adopt without any outside intervention. We show that, without vaccination, MPX can become endemic in previously non-endemic regions, including the United States. We also show that to "not vaccinate" is often an optimal solution from the individual's perspective. Moreover, we demonstrate that, for some parameter values, there are multiple equilibria of the vaccination game, and they exhibit a backward bifurcation. Thus, without centrally mandated minimal vaccination rates, the population could easily revert to no vaccination scenario.

Complex Network Analysis of Mass Violation, Specifically Mass Killing

News reports in media contain news about society’s social and political conditions. With the help of publicly available digital datasets of events, it is possible to study a complex network of mass violations, i.e., Mass Killings. Multiple approaches have been applied to bring essential insights into the events and involved actors. Power law distribution behavior finds in the tail of actor mention, co-actor mention, and actor degree tells us about the dominant behavior of influential actors that grows their network with time. The United States, France, Israel, and a few other countries have been identified as major players in the propagation of Mass Killing throughout the past 20 years. It is demonstrated that targeting the removal of influential actors may stop the spreading of such conflicting events and help policymakers and organizations. This paper aims to identify and formulate the conflicts with the actor’s perspective at a global level for a period of time. This process is a generalization to be applied to any level of news, i.e., it is not restricted to only the global level.

Game Theory in Defence Applications: A Review

This paper presents a succinct review of attempts in the literature to use game theory to model decision-making scenarios relevant to defence applications. Game theory has been proven as a very effective tool in modelling the decision-making processes of intelligent agents, entities, and players. It has been used to model scenarios from diverse fields such as economics, evolutionary biology, and computer science. In defence applications, there is often a need to model and predict the actions of hostile actors, and players who try to evade or out-smart each other. Modelling how the actions of competitive players shape the decision making of each other is the forte of game theory. In past decades, there have been several studies that applied different branches of game theory to model a range of defence-related scenarios. This paper provides a structured review of such attempts, and classifies existing literature in terms of the kind of warfare modelled, the types of games used, and the players involved. After careful selection, a total of 29 directly relevant papers are discussed and classified. In terms of the warfares modelled, we recognise that most papers that apply game theory in defence settings are concerned with Command and Control Warfare, and can be further classified into papers dealing with (i) Resource Allocation Warfare (ii) Information Warfare (iii) Weapons Control Warfare, and (iv) Adversary Monitoring Warfare. We also observe that most of the reviewed papers are concerned with sensing, tracking, and large sensor networks, and the studied problems have parallels in sensor network analysis in the civilian domain. In terms of the games used, we classify the reviewed papers into papers that use non-cooperative or cooperative games, simultaneous or sequential games, discrete or continuous games, and non-zero-sum or zero-sum games. Similarly, papers are also classified into two-player, three-player or multi-player game based papers. We also explore the nature of players and the construction of payoff functions in each scenario. Finally, we also identify gaps in literature where game theory could be fruitfully applied in scenarios hitherto unexplored using game theory. The presented analysis provides a concise summary of the state-of-the-art with regards to the use of game theory in defence applications and highlights the benefits and limitations of game theory in the considered scenarios.

A generative network model of neurodevelopmental diversity in structural brain organization

The formation of large-scale brain networks, and their continual refinement, represent crucial developmental processes that can drive individual differences in cognition and which are associated with multiple neurodevelopmental conditions. But how does this organization arise, and what mechanisms drive diversity in organization? We use generative network modeling to provide a computational framework for understanding neurodevelopmental diversity. Within this framework macroscopic brain organization, complete with spatial embedding of its organization, is an emergent property of a generative wiring equation that optimizes its connectivity by renegotiating its biological costs and topological values continuously over time. The rules that govern these iterative wiring properties are controlled by a set of tightly framed parameters, with subtle differences in these parameters steering network growth towards different neurodiverse outcomes. Regional expression of genes associated with the simulations converge on biological processes and cellular components predominantly involved in synaptic signaling, neuronal projection, catabolic intracellular processes and protein transport. Together, this provides a unifying computational framework for conceptualizing the mechanisms and diversity in neurodevelopment, capable of integrating different levels of analysis-from genes to cognition.

Optimal governance and implementation of vaccination programmes to contain the COVID-19 pandemic

Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public. We emphasize that decision-making under uncertainty and imperfect information, and with only conditionally optimal outcomes, is a unique forte of established game-theoretic modelling. Therefore, we can use this approach to obtain the best framework for modelling and simulating vaccination prioritization and uptake that will be readily available to inform important policy decisions for the optimal control of the COVID-19 pandemic.

Prediction and prevention of disproportionally dominant agents in complex networks

Proportional growth is the driver behind the dynamics of a large class of complex networks. However, if left uncontrolled a few agents may become so dominant that their actions compromise the entire system. We present a framework that monitors the system’s distance from such imbalanced states. When the system approaches an imbalanced state, we show how to structure an optimal, cost-efficient intervention policy. Focusing only on either helping the least-fit agents or punishing the most dominant ones in isolation turns out to be inefficient. Instead, our results call for a more wholistic approach, with important implications for the structure of regulatory matters such as antitrust policies, taxation law, subsidies, or development aid.

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.

Testing "efficient supply chain propositions" using topological characterization of the global supply chain network

In this paper, we study the topological properties of the global supply chain network in terms of its degree distribution, clustering coefficient, degree-degree correlation, bow-tie structure, and community structure to test the efficient supply chain propositions proposed by E. J.S. Hearnshaw et al. The global supply chain data in the year 2017 are constructed by collecting various company data from the web site of Standard & Poor’s Capital IQ platform. The in- and out-degree distributions are characterized by a power law of the form of γ_in = 2.42 and γ_out = 2.11. The clustering coefficient decays 〈C(k)〉∼k-βk with an exponent β_k = 0.46. The nodal degree-degree correlations 〈k_nn(k)〉 indicates the absence of assortativity. The bow-tie structure of giant weakly connected component (GWCC) reveals that the OUT component is the largest and consists 41.1% of all firms. The giant strong connected component (GSCC) is comprised of 16.4% of all firms. We observe that upstream or downstream firms are located a few steps away from the GSCC. Furthermore, we uncover the community structures of the network and characterize them according to their location and industry classification. We observe that the largest community consists of the consumer discretionary sector based mainly in the United States (US). These firms belong to the OUT component in the bow-tie structure of the global supply chain network. Finally, we confirm the validity of Hearnshaw et al.’s efficient supply chain propositions, namely Proposition S1 (short path length), Proposition S2 (power-law degree distribution), Proposition S3 (high clustering coefficient), Proposition S4 (“fit-gets-richer” growth mechanism), Proposition S5 (truncation of power-law degree distribution), and Proposition S7 (community structure with overlapping boundaries) regarding the global supply chain network. While the original propositions S1 just mentioned a short path length, we found the short path from the GSCC to IN and OUT by analyzing the bow-tie structure. Therefore, the short path length in the bow-tie structure is a conceptual addition to the original propositions of Hearnshaw.

Raising the Connectome: The Emergence of Neuronal Activity and Behavior in Caenorhabditis elegans

The differentiation of neurons and formation of connections between cells is the basis of both the adult phenotype and behaviors tied to cognition, perception, reproduction, and survival. Such behaviors are associated with local (circuits) and global (connectome) brain networks. A solid understanding of how these networks emerge is critical. This opinion piece features a guided tour of early developmental events in the emerging connectome, which is crucial to a new view on the connectogenetic process. Connectogenesis includes associating cell identities with broader functional and developmental relationships. During this process, the transition from developmental cells to terminally differentiated cells is defined by an accumulation of traits that ultimately results in neuronal-driven behavior. The well-characterized developmental and cell biology of Caenorhabditis elegans will be used to build a synthesis of developmental events that result in a functioning connectome. Specifically, our view of connectogenesis enables a first-mover model of synaptic connectivity to be demonstrated using data representing larval synaptogenesis. In a first-mover model of Stackelberg competition, potential pre- and postsynaptic relationships are shown to yield various strategies for establishing various types of synaptic connections. By comparing these results to what is known regarding principles for establishing complex network connectivity, these strategies are generalizable to other species and developmental systems. In conclusion, we will discuss the broader implications of this approach, as what is presented here informs an understanding of behavioral emergence and the ability to simulate related biological phenomena.

Investigating the Influence of Inverse Preferential Attachment on Network Development

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.

Detecting differences in the topology of scale-free networks grown under time-dynamic topological fitness

The fitness model was introduced in the literature to expand the Barabasi-Albert model’s generative mechanism, which produces scale-free networks under the control of degree. However, the fitness model has not yet been studied in a comprehensive context because most models are built on invariant fitness as the network grows and time-dynamics mainly concern new nodes joining the network. This mainly static consideration restricts fitness in generating scale-free networks only when the underlying fitness distribution is power-law, a fact which makes the hybrid fitness models based on degree-driven preferential attachment to remain the most attractive models in the literature. This paper advances the time-dynamic conceptualization of fitness, by studying scale-free networks generated under topological fitness that changes as the network grows, where the fitness is controlled by degree, clustering coefficient, betweenness, closeness, and eigenvector centrality. The analysis shows that growth under time-dynamic topological fitness is indifferent to the underlying fitness distribution and that different topological fitness generates networks of different topological attributes, ranging from a mesh-like to a superstar-like pattern. The results also show that networks grown under the control of betweenness centrality outperform the other networks in scale-freeness and the majority of the other topological attributes. Overall, this paper contributes to broadening the conceptualization of fitness to a more time-dynamic context.

Network effects govern the evolution of maritime trade

Maritime transport accounts for over 80% of the world trade volume and is the backbone of the global economy. Global supply chains create a complex network of trade flows. The structure of this network impacts not only the socioeconomic development of the concerned regions but also their ecosystems. The movements of ships are a considerable source of CO₂ emissions and contribute to climate change. In the wake of the announced development of Arctic shipping, the need to understand the behavior of the maritime trade network and to predict future trade flows becomes pressing. We use a unique database of daily movements of the world fleet over the period 1977-2008 and apply machine learning techniques on network data to develop models for predicting the opening of new shipping lines and for forecasting trade volume on links. We find that the evolution of this system is governed by a simple rule from network science, relying on the number of common neighbors between pairs of ports. This finding is consistent over all three decades of temporal data. We further confirm it with a natural experiment, involving traffic redirection from the port of Kobe after the 1995 earthquake. Our forecasting method enables researchers and industry to easily model effects of potential future scenarios at the level of ports, regions, and the world. Our results also indicate that maritime trade flows follow a form of random walk on the underlying network structure of sea connections, highlighting its pivotal role in the development of maritime trade.

Applications of Game Theory in Project Management: A Structured Review and Analysis

This paper provides a structured literature review and analysis of using game theory to model project management scenarios. We select and review thirty-two papers from Scopus, present a complex three-dimensional classification of the selected papers, and analyse the resultant citation network. According to the industry-based classification, the surveyed literature can be classified in terms of construction industry, ICT industry or unspecified industry. Based on the types of players, the literature can be classified into papers that use government-contractor games, contractor–contractor games, contractor-subcontractor games, subcontractor–subcontractor games or games involving other types of players. Based on the type of games used, papers using normal-form non-cooperative games, normal-form cooperative games, extensive-form non-cooperative games or extensive-form cooperative games are present. Also, we show that each of the above classifications plays a role in influencing which papers are likely to cite a particular paper, though the strongest influence is exerted by the type-of-game classification. Overall, the citation network in this field is sparse, implying that the awareness of authors in this field about studies by other academics is suboptimal. Our review suggests that game theory is a very useful tool for modelling project management scenarios, and that more work needs to be done focusing on project management in ICT domain, as well as by using extensive-form cooperative games where relevant.

Assortativity and mixing patterns in international supply chain networks

As economic globalisation increases, inclination toward domestic protectionism is also increasing in many countries of the world. To improve the productivity and the resilience of national economies, it is important to understand the drivers and the barriers of the internatiolisation of economic activities. While internatiolisation of individual economic actors is difficult to explain using traditional theories, aggregate patterns may be explained to some extent. We take a network-centric perspective to describe the extent of corporate internatiolisation in different countries. Based on Newman's assortativity coefficient, we design a range of assortativity metrics which are appropriate in the firm network context. Using these, we quantify companies' appetite for internatiolisation in relation to the internatiolisation of their partners. We use the Factset Revere dataset, which is provided by FactSet Research Systems Inc., that captures global supply chain relationships between companies. We identify countries where the level of internationalisation is relatively high or relatively low, and we show that subtle differences in the assortativity metrics used change the ranking of countries significantly in terms of the assortativity correlation, highlighting that companies in different countries are prone to different types of internationalisation. Overall, we demonstrate that firms from most countries in the dataset studied have a slight preference to make supply chain relationships with other firms which have undergone a similar level of internationalisation, and other firms from their own country. The implications of our results are important for countries to understand the evolution of international relationships in their corporate environments, and how they compare to other nations in the world in this regard.

Morphogenesis of Urban Water Distribution Networks: A Spatiotemporal Planning Approach for Cost-Efficient and Reliable Supply

Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects of demand shifting and flow rearrangements are simulated and assessed with hydraulic performances. With the methodology, it is possible to test various planning and adaptation options of the future WDN, where the unknown (future) network is approximated via the co-located and known (future) road network, and hence different topological characteristics (branched vs. strongly looped layout) can be investigated. The reliability of the planning options is evaluated with the flow entropy, a measure based on Shannon’s informational entropy. Uncertainties regarding future water consumption and water loss management are included in a scenario analysis. To avoid insufficient water supply to customers during the transition process from an initial to a final WDN state, an adaptation concept is proposed where critical WDN components are replaced over time. Finally, the method is applied to the drastic urban transition of Kiruna, Sweden. Results show that without adaptation measures severe performance drops will occur after the WDN state 2023, mainly caused by the disconnection of WDN parts. However, with low adaptation efforts that consider 2–3% pipe replacement, sufficient pressure performances are achieved. Furthermore, by using an entropy-cost comparison, the best planning options are determined.

Mechanisms of complex network growth: Synthesis of the preferential attachment and fitness models

We analyze growth mechanisms of complex networks and focus on their validation by measurements. To this end we consider the equation ΔK=A(t)(K+K_{0})Δt, where K is the node's degree, ΔK is its increment, A(t) is the aging constant, and K_{0} is the initial attractivity. This equation has been commonly used to validate the preferential attachment mechanism. We show that this equation is undiscriminating and holds for the fitness model [Caldarelli et al., Phys. Rev. Lett. 89, 258702 (2002)PRLTAO0031-900710.1103/PhysRevLett.89.258702] as well. In other words, accepted method of the validation of the microscopic mechanism of network growth does not discriminate between "rich-gets-richer" and "good-gets-richer" scenarios. This means that the growth mechanism of many natural complex networks can be based on the fitness model rather than on the preferential attachment, as it was believed so far. The fitness model yields the long-sought explanation for the initial attractivity K_{0}, an elusive parameter which was left unexplained within the framework of the preferential attachment model. We show that the initial attractivity is determined by the width of the fitness distribution. We also present the network growth model based on recursive search with memory and show that this model contains both the preferential attachment and the fitness models as extreme cases.

Network science approach to modelling the topology and robustness of supply chain networks: a review and perspective

Due to the increasingly complex and interconnected nature of global supply chain networks (SCNs), a recent strand of research has applied network science methods to model SCN growth and subsequently analyse various topological features, such as robustness. This paper provides: (1) a comprehensive review of the methodologies adopted in literature for modelling the topology and robustness of SCNs; (2) a summary of topological features of the real world SCNs, as reported in various data driven studies; and (3) a discussion on the limitations of existing network growth models to realistically represent the observed topological characteristics of SCNs. Finally, a novel perspective is proposed to mimic the SCN topologies reported in empirical studies, through fitness based generative network models.