Complex Networks & Their Applications XII

Integral to the problem of detecting communities through graph clustering is the expectation that they are “well-connected”. Surprisingly, we find that the output of multiple clustering approaches–the Leiden algorithm with either the Constant Potts Model or modularity as quality function, Iterative K-Core Clustering, Infomap, and Markov Clustering–include communities that fail even a mild requirement for well-connectedness. As a remediation strategy, we have developed the “Connectivity Modifier” (CM), which iteratively removes small edge cuts and re-clusters until all communities detected are well-connected. Results from real-world networks with up to 75,025,194 nodes illustrate how CM enables additional insights into community structure within networks, while results on synthetic networks show that the CM algorithm improves accuracy in recovering true communities. Our study also raises questions about the “clusterability” of networks and mathematical models of community structure.

A network autocorrelation model may be embedded within a hierarchical data structure involving a complex network, when the peer effect (also referred to as social influence or contagion) is believed to act between units (e.g., hospitals) above the level at which data is observed. We develop two hierarchical network autocorrelation models to represent peer effects between hospitals when modeling individual outcomes of the patients who attend those hospitals. We use a Bayesian approach for model estimation and assess the performance of the models and sensitivity of results to different prior distributions using a simulation study. We construct a United States New England region patient-sharing hospital network and apply our models and Bayesian estimation procedures to study the diffusion of the adoption of robotic surgery and hospital-peer effects in the quality of patients outcomes using a cohort of United States Medicare beneficiaries in 2016 and 2017.

We propose a model for network community detection using topological data analysis, a branch of modern data science that leverages theory from algebraic topology to statistical analysis and machine learning. Specifically, we use cellular sheaves, which relate local to global properties of various algebraic topological constructions, to propose three new algorithms for vertex clustering over networks to detect communities. We apply our algorithms to real social network data in numerical experiments and obtain near optimal results in terms of modularity. Our work is the first implementation of sheaves on real social network data and provides a solid proof-of-concept for future work using sheaves as tools to study complex systems captured by networks and simplicial complexes.

Communities are often defined as sets of nodes that are more densely connected to each other than to those outside the community, i.e., high-modularity partitions. It seems obvious that isolating high-modularity communities is a good way to prevent the spread of cascading failures. Here we develop a heuristic approach informed by Moore-Shannon network reliability that focuses on dynamics rather than topology. It defines communities directly in terms of the size of cascades they allow. We demonstrate that isolating communities defined this way may control cascading failure better. Moreover, this approach is sensitive to the values of dynamical parameters and allows for problem-specific constraints such as cost.

In this paper we explore the role of matrix scaling on a matrix of counts when building a topic model using non-negative matrix factorization. We present a scaling inspired by the normalized Laplacian (NL) for graphs that can greatly improve the quality of a non-negative matrix factorization. The results parallel those in the spectral graph clustering work of [12], where the authors proved adjacency spectral embedding (ASE) spectral clustering was more likely to discover core-periphery partitions and Laplacian Spectral Embedding (LSE) was more likely to discover affinity partitions. In text analysis non-negative matrix factorization (NMF) is typically used on a matrix of co-occurrence “contexts” and “terms” counts. The matrix scaling inspired by LSE gives significant improvement for text topic models in a variety of datasets. We illustrate how matrix scalings in NMF can dramatically improve the quality of a topic model on three datasets where human annotation is available. Using the adjusted Rand index (ARI), a measure cluster similarity we see an increase of 50% for Twitter data and over 200% for a newsgroup dataset versus using counts, which is the analogue of ASE. For clean data, such as those from the Document Understanding Conference, NL gives over 40% improvement over ASE. We conclude with some analysis of this phenomenon and some connections of this scaling with other matrix scaling methods.

In recent decades, several community detection methods have been proposed to uncover densely connected groups in a network. In many cases, there is the necessity of detecting such a group around a seed node that may be of particular topological importance or the external knowledge enable that node to be significant for the specific subgroup. In this way, local community detection algorithms can discover subgroups faster than global community detection algorithms that cover the entire network. This study aims to introduce new variants of an existing local community detection algorithm that uncover a single community and establish the positive aspects of identifying better communities. We experimentally evaluate our proposed methods in synthetic and real datasets compared to the baseline method, three state-of-the-art methods in local community detection, and a global community detection method.

The significance of pyramid structures in dominating social networks is often mentioned, but the concept lacks a precise definition and comprehensive empirical analysis. To fill this gap, this paper offers a rigorous definition of pyramid structure, characterizing it as an expanding rooted tree. Empirical evidence, drawn from an extensive study of real-world social networks, corroborates existing hypotheses about the prevalence of large pyramid structures in such networks. Additionally, we identify a unique network characteristic: pyramid sizes vary across different types of networks. This finding suggests that existing models may not be sufficient for accurately representing real-world social networks and calls for the development of a new model. The paper also explores more characteristics and applications of pyramid in developing network metrics and structures, touching on aspects like degree distribution, clustering coefficient, core-periphery structures, and small-world networks.

The structural organization of supply networks plays an important role in their functioning. In this work, we discuss how standard community detection analysis can be complemented by the definition of communities in the networks’ plane dual. Such communities are characterized not by weak but by strong connectivity between the different components of the network. We extract dual communities in leaf venation networks, finding that they can reveal structural features not visible to traditional community detection methods. Furthermore, we show that the presence of dual community structures suppresses failure spreading and that dual communities can be used to classify different leaf types.

Analysts interested in understanding the community structure of a particular real-world network will often simply choose a popular community detection algorithm and trust the generated results without further investigation, but algorithm performance can vary depending on the network characteristics. We demonstrate that by running experiments on benchmark graphs tailored to match characteristics of a real-world network of interest, a better understanding can be obtained on how community detection algorithms will perform on the real-world network. We show that the correlation between the performance of the community detection methods on a publicly available dataset to the average performance of the same methods on the corresponding tailored benchmark graphs is high whereas the correlation with LFR benchmark graphs is negative. This means the methods that performed well on the tailored graphs also performed well on the real-world network but methods that perform well on LFR graphs did not perform well on the real-world network, demonstrating that the proposed methodology has merit.

Funding agencies and researchers are placing increasing emphasis on interdisciplinary research (IDR) to promote innovation and to address complex real-world problems. Understanding characteristics of IDR early (as soon as projects get funded), can formatively shape a research community at portfolio, project, and individual investigator levels. This involves surfacing the interacting components and the context that manifest IDR. We present a network-based methodology to model and analyze IDR, and apply it to a three-year portfolio of awards in the Research on Emerging Technologies for Teaching and Learning program. Our IDR analysis features two network-based metrics (1) diversity of expertise and (2) intensity of inter-expertise collaboration. It reveals the organization of the 116 expertise areas that form the “building blocks” for IDR in this community, while also highlighting potential for knowledge integration, specifically within “hotspot” topics. It also reveals gaps in IDR potential. Applying our network-based methodology for understanding IDR could enable other research domains and communities to conduct early and rapid analyses of the emerging IDR profile in their network, and could inform formative efforts to strengthen IDR.

A community structure that is often present in complex networks plays an important role not only in their formation but also shapes dynamics of these networks, affecting properties of their nodes. In this paper, we propose a family of community-aware node features and then investigate their properties. We show that they have high predictive power for classification tasks. We also verify that they contain information that cannot be recovered completely neither by classical node features nor by classical or structural node embeddings.

Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models. These methods suffer from assuming temporal stationarity and are influenced by the granularity of observation intervals.In this study, we propose an approach based on the signature matrix, a concept from path theory for studying stochastic processes. By employing a signature-derived similarity measure, our method overcomes drawbacks of traditional correlation-based techniques.Through a series of numerical experiments, we demonstrate that our method consistently yields higher modularity compared to baseline models, when tested on the Standard and Poor’s 500 dataset. Moreover, our approach showcases enhanced stability in modularity when the length of the underlying time series is manipulated.This research contributes to the field of community detection by introducing a signature-based similarity measure, offering an alternative to conventional correlation matrices.

Real-world networks often contain community structures, where nodes form tightly interconnected clusters. Recent research indicates hierarchical organization, where vertices split into groups that further subdivide across multiple scales. However, individuals in social networks typically belong to multiple communities due to their various affiliations, such as family, friends, and colleagues. These overlaps will emerge in the community structure of online social networks and other complex networks like in biology, where nodes have diverse functions. In this work, we propose an algorithm for hierarchical overlapping community detection in weighted networks. The overlap between clusters is realized via maximal cliques that are used as base elements for hierarchical agglomerative clustering on the graph (GHAC). The closed trail distance and the size of the maximal clique in overlap are used for the dissimilarity between clusters in agglomerative steps of the GHAC. The closed trail distance is designed for weighted networks.Experiments on synthetic networks and different evaluations of the results of experiments show that the proposed algorithm is comparable with other widely used algorithms for overlapping community detection and is efficient for detecting hierarchy structure in weighted networks.

Identifying sub-networks showing similar properties, referred to as community detection, is a challenging task in network analysis. This challenge becomes even more formidable in bipartite networks. The focus of this study is the patients with problems in their Peripheral Nerve System. To this aim, we engaged the assistance of spinal specialty clinics in the collection of necessary Data. We employ the bipartite network to represent the relationship between the patients and their symptoms and disorders. The resulting bipartite network showcases unequally sized sets of nodes, making community detection more challenging. The principal purpose of this study is to develop a new, practically relevant method for finding communities inside such networks. As such, we propose the Bi-MRComSim algorithm which applies different methods to transform the bipartite network to a unipartite one that can find meaningful communities between patients that coincide 85% of the time with diagnoses issued by physicians.

The gradient descent has proven to be an effective optimization strategy. The current research proposes a novel clustering methodology using this strategy to recover communities in feature-rich networks. Our adoption of this strategy did not lead to promising results, and thus to improve them, we propose a special “refinement” mechanism, which culls out potentially misleading objects during the optimization. We validated and compared our proposed methods with three state-of-the-art algorithms over four real-world and 160 synthetic data sets. Our results proved that our proposed method is valid and in the majority of cases has a significant edge over the competitors.

The study of complete sub-graphs belongs to the classical problems of graph theory. Thanks to sociology, the term clique has come to be used for structures representing a small group of people or other entities who share common characteristics and know each other. Clique detection algorithms can be applied in all domains where networks are used to describe relationships among entities. That is not only in social, information, or communication networks but also in biology, chemistry, medicine, etc. In large-scale, e.g., social networks, cliques can have hundreds or more nodes. On the other hand, e.g., in co-authorship networks representing publishing activities of groups of authors, cliques contain, at most, low dozens of nodes. Our paper describes experiments on detecting strong cliques in two weighted co-authorship networks. These experiments are motivated by the assumption that not every clique detected by traditional algorithms truly satisfies the sociological assumption above. Informally speaking, the approach presented in this paper assumes that each pair of clique nodes must be closer to each other and other clique nodes than to non-clique nodes. Using experiments with weighted co-authorship networks, we show how clique detection results differ from the traditional approach when both the strength of the edge (weight) and the structural neighborhood of the clique are considered simultaneously in the analysis.

Community structure is a critical feature of real networks, providing insights into nodes’ internal organization. Nowadays, with the availability of highly detailed temporal networks such as link streams, studying community structures becomes more complex due to increased data precision and time sensitivity. Despite numerous algorithms developed in the past decade for dynamic community discovery, assessing their performance on link streams remains a challenge. Synthetic benchmark graphs are a well-accepted approach for evaluating static community detection algorithms. Additionally, there have been some proposals for slowly evolving communities in low-resolution temporal networks like snapshots. Nevertheless, this approach is not yet suitable for link streams. To bridge this gap, we introduce a novel framework that generates synthetic modular link streams with predefined communities. Subsequently, we evaluate established dynamic community detection methods to uncover limitations that may not be evident in snapshots with slowly evolving communities. While no method emerges as a clear winner, we observe notable differences among them.

The detection of community structure is probably one of the central challenges in complex networks whose objective is to identify internal organizations of people, molecules or processes within a network. The issue is to provide a network partition representative of this organization so that each community presumably gathers nodes sharing a common mission, purpose or property. Usually, this identification is based on the difference in connectivity density between the interior and border of a community. Indeed, nodes sharing a common purpose or property are expected to interact closely. Although this rule appears mostly relevant, some fundamental scientific problems like disease module detection highlight the inability to meaningfully determine the communities by this connectivity rule. The main reason is that the connectivity density may not be correlated to a shared property or purpose. Another paradigm is therefore necessary to properly formalize this problem in order to accurately detect these communities. In this article we propose a new framework to study this novel community formation property. Considering that colors formally represent shared properties, the problem becomes to maximize groups of nodes of the same color within communities. We introduce a new measurement called chromatic entropy assessing the quality of the community structure regarding the color constraint. Next we propose a novel algorithm detecting the community structure based on this new community formation paradigm.

In an era of global interconnectedness, transportation networks serve as vital conduits for international relations, trade, and cultural exchange. Previous research has extensively examined the worldwide air transportation network at three distinct levels: global, regional, and national, with contributions from various researchers shedding light on different facets of the network. Focusing on densely connected regions that extend from other dense areas, this study unveils the hierarchical structure of the global air transport network. Results emphasize the multi-level nature of the network, from significant regions to country-based divisions and ultimately to the intricate hub-and-spoke model. One observes increased hub dominance and negative assortativity values as one delves deeper into the network’s hierarchy. This investigation brings a more comprehensive understanding of the global air transport network and its intricate hierarchical organization.

The topological structure of the world air transportation network is the subject of much research. This paper reports a comparative analysis of the weighted and unweighted air transportation network at the mesoscopic level. We use the component structure to isolate regional from interregional traffic and infrastructure. Recently introduced in the network literature, the component structure splits the network into local and global components. The local components are the dense parts of the network. They capture the regional flights. The global components linking the dense parts capture the inter-regional flights. Results display fewer local components well delimited and more global components covering the world than the unweighted world air transportation network. Beyond their structural implications, these components offer practical advantages. They can be a foundation for optimizing transportation routes and schedules, leading to cost savings and reduced travel times. Stakeholders in transportation, including airlines, shipping companies, urban planners, and policymakers, can leverage this knowledge to make informed decisions and strategic plans that promote economic growth and environmental sustainability.

Given a defined set of communities, modularity is computed by comparing each existing edge with its probability of occurrence in a random graph null model. The heuristic has historically garnered a wealth of attention, and many community detection algorithms have been designed around maximizing modularity. Despite this, there are potential issues with the Chung-Lu null graph model that underpins the heuristic. In this manuscript, we explore the output communities given by modularity maximization when this null model is subject to change. We construct two null models using iterated double edge swapping and maximum likelihood estimation, and we use these models as the basis for new modularity-like heuristics we call desmod, and mlemod. We compare the clusters output by standard modularity maximization with those output by our methods on a test suite of LFR benchmark graphs and find that changing the null model consistently increases the normalized mutual information scores when the mixing parameter is high.

This study explores the mesoscopic intricacies governing the interplay of regional and interregional traffic flows within the world air transportation network. We adopt a network decomposition method, the component structure, to partition the network into local and global components, aligning with geographical and cultural boundaries. We explore the centrality and the core of these unweighted and weighted networks. The analysis of centrality highlights distinctions between airports with high traffic and those with high degrees. This contrast is particularly pronounced in the global air network and its largest component. Additionally, core analysis reveals similarities between the s-core and the k-core for local and global components, despite the latter encompassing more airports. In the world air network, North and Central America-Caribbean airports dominate the s-core, while European airports take precedence in the k-core. Interestingly, airports distant from their component’s core can also rank among the top high-strength airports. This comparative analysis underscores the component structure representation’s vital role in uncovering regional and interregional dynamics within the world air transportation network, providing valuable insights into its mesoscopic structure and implications for global air travel.Moreover, we explore the strength and the s-core of these networks. Results display fewer local components well delimited and more global components covering the world than the unweighted world air transportation network. Centrality analysis reveals the difference between the top airports with high traffic and the top airports with high degrees. This difference is more pronounced in the global air network and the largest global component. Core analysis shows similitude between the s-core and the k-core for the local and global components, even though the latter includes more airports. For the world air network, the North and Central America-Caribbean airports dominate the s-core, whereas the European airports dominate the k-core. Transport network and its intricate hierarchical organization.

We present two new seeding strategies for the Influence Maximization Problem for Viral Marketing, based on graph connectivity and spectral graph theory. Specifically, the first approach CVSP uses the cut vertices and the separation pairs as the starting seeds. The second approach ER uses the vertex ranking based on the effective resistance values of the incident edges. CVSP and ER are efficient, and can be implemented in linear and near linear time, respectively.Experiments using the Independent Cascade diffusion model with real-world data sets show that our new seeding strategies perform significantly better than the existing methods, such as centrality measures, k-core and the state-of-the-art IMM, in particular for the scale-free networks with globally sparse, locally dense clusters with small diameters, in the final influence spread. Moreover, visual analysis enables more refined comparison between the methods, demonstrating that our methods have more globally wide influence spread pattern than other methods with locally dense influence spread pattern.

We examine how homophily widely observed in networks affects epidemic processes on networks, which are often used to model the spread of information and diseases in social networks and of malware and viruses in information systems. We propose a new framework for modeling the effects of homophily with the help of multi-type branching processes. Using this framework we derive conditions that tell us how homophily influences the likelihood of suffering an epidemic. Finally, we present numerical studies to verify our findings.

Human papillomaviruses (HPV) are among the most common sexually transmitted infections and a necessary cause of cervical cancer. In the context of vaccination against a sub-group of genotypes, better understanding the respective role of biological interactions between HPV genotypes and social interactions between humans is essential to anticipate what the vaccine impact could be at the population level. Here, we present a novel stochastic agent-based model formalizing the co-circulation on a human partnership network of multiple interacting genotypes, some of them being preventable by the vaccine (vaccine types) and others not. The model explicitly formalizes heterogeneity in sexual behaviors and allows exploration of distinct genotypic interaction mechanisms during intra-host co-infections. Using model simulations, we investigate infection dynamics after vaccine introduction in the population depending on assumptions about vaccine coverage and interactions between vaccine and non-vaccine genotypes.

Peste des Petits Ruminants (PPR) is a highly contagious disease affecting sheep and goats and spreading through livestock movements. The FAO and WOAH have set the goal to eradicate it by 2030, with one of the key steps being the improvement of surveillance networks. In our study, we utilize an SI model to simulate the spread of PPR across three Nigerian States due to animal movements. Our objective is to identify areas that could serve as potential sentinel nodes, which are nodes that may become infected promptly at the onset of epidemics. We reconstructed the mobility network using (the partial) movement data collected through market surveys. Due to the limitations of the study, we implement plausible network modifications and generated eight distinct network configurations. For each of these configurations, we assessed the extent of the epidemics, the presence of recurrent patterns and characterize sentinel nodes. Our findings indicate that minor network modifications do not impact the final sizes of epidemics. However, removing a central market or introducing a significant number of new links can lead to noticeable shifts in epidemic propagation trajectories. Regardless of the specific configurations considered, we identified three clusters of epidemic origins, each exhibiting distinct behaviors. Nevertheless, geographical proximity among these origins does not necessarily imply similar transmission patterns. Furthermore, our study highlights that, in most configurations, attributes such as the in-H index, eigenvector and in-degree centralities emerge as the most influential factors in defining vulnerable nodes. Therefore, we recommend prioritizing data collection efforts in central markets due to their wealth of information resources

In the pursuit of accurate infectious disease forecasting, micro-level contact modeling in contact networks emerges as a pivotal element. This research delves into the intricacies of nuanced micro-level modeling, presenting adaptable models tailored for specific locations, derived from a refined travel demand model. In our experiments, we observed that varied encounter patterns among individuals directly influence infection dynamics. Additionally, we observe distinct trends in the spreading dynamics between temporal dynamic networks and their static counterparts for certain encounter models. The study underscores the need for a deeper appreciation of micro-level encounter patterns in epidemiological modeling. Such understanding is pivotal in shaping effective interventions and public health strategies during pandemic scenarios.

People who inject drugs (PWID) are part of HIV/AIDS risk networks, where individuals can engage in sexual and injection risk behavior. Low socioeconomic status and lack of access to medical care often complicate successful engagement in HIV care for PWID. This study investigates how locus of control and self-blame regarding HIV/AIDS risk affects health-seeking behavior in PWID participants and their community members. We apply causal inference methodology to PWID HIV risk networks ascertained from the Social Factors and HIV Risk Study (SFHR) conducted between 1991 and 1993 in Bushwick, Brooklyn, New York. We found estimated protective disseminated effects of attitudes toward HIV/AIDS on health-seeking behaviors of others in the PWID community. A positive attitude toward controlling HIV/AIDS can improve the health-seeking behavior of other members in the community with a pessimistic attitude toward HIV/AIDS control. Interventions to improve attitudes toward HIV/AIDS risk can boost health-seeking behavior among both PWID receiving the intervention themselves and other unexposed PWID in the community.

Understanding how cooperation spreads across social groups is fundamental in predicting how people will interact with each other in relation to the use and exploitation of the resources they are provided with. When social interactions can be mapped to a network, questions arise about the impact of the connection structure which can benefit from the literature developed for a dynamical systems. One model that is widely used as a model to understand the dynamics of cooperation is the replicator equation. While research has been proposed to adapt that equation to a structured graph, we offer a straightforward approach by benefiting from the networked SI diffusion model and replicator equation to create a replicator equation on a network with state-dependent diffusive constant. This approach can be applied to any network structure and features separation of the game and the information diffusion mechanism. The equilibria towards which the system evolves are here characterised and discussed.

The Electronic messaging is a widely used network application, and the user’s authentication is a necessary aspect. Commonly employed approaches include PKI and S/MIME encryption protocols for email, but have many security threats, such as EFAIL and attack MITM attack. The innovative property of blockchain minimizes these threats and provides decentralized sensitive operations along with high security. It terminates the need of trusted intermediaries. Smart contracts are implementation of second generation of blockchain technology. The objective of our work is to provide a secure peer to peer messaging solution. In this paper, we explain how blockchain would ensure secure communications, and also, we have designed a model for messaging system that ensures good performance and data security which verifies the user identities and their public keys, and also validate the user certificate. The proposed messaging system is decentralized in nature and allows secure messages exchange.

The Conference of Parties (COP) aims to address the global warming problem through agreements for reducing emissions. However, the current strategies fall short due to minimal efforts for emission reductions driven by short-term economic considerations. To better understand under which circumstances countries may have more virtuous behavior, we propose a static game model. In this model, the players are represented by governments, and their actions correspond to emissions levels. The utilities are a trade-off between economic benefits and damage caused by climate change. A key feature of the game is that it is parameterized by a state, which is precisely the state of the climate dynamics. We conduct the Nash equilibrium analysis. In the numerical analysis, we assess the impact of the damage function on the behavior of the governments.

The modelling of stochastic linear systems in large complex networks is intractable computationally and may be impossible due to data-collection costs or privacy concerns. Graphon theory provides an approach to overcome these issues by providing potentially simple limit objects for infinite sequences of graphs, permitting one to approximate arbitrarily large networks by infinite dimensional operators. Graphon system theory is extended here to stochastic systems by the use of Q-noise, a generalization of Wiener processes in finite dimensional spaces to processes in function spaces. The theory is developed for low rank systems as a special case.

Uniform sampling from the set $$\mathcal {G}(\textbf{d})$$ G ( d ) of graphs with a given degree-sequence $$\textbf{d} = (d_1, \dots , d_n) \in \mathbb N^n$$ d = ( d 1 , ⋯ , d n ) ∈ N n is a classical problem in the study of random graphs. We consider an analogue for temporal graphs in which the edges are labeled with integer timestamps. The input to this generation problem is a tuple $$\textbf{D} = (\textbf{d}, T) \in \mathbb N^n \times \mathbb N_{>0}$$ D = ( d , T ) ∈ N n × N > 0 and the task is to output a uniform random sample from the set $$\mathcal {G}(\textbf{D})$$ G ( D ) of temporal graphs with degree-sequence $$\textbf{d}$$ d and timestamps in the interval [1, T]. By allowing repeated edges with distinct timestamps, $$\mathcal {G}(\textbf{D})$$ G ( D ) can be non-empty even if $$\mathcal {G}(\textbf{d})$$ G ( d ) is, and as a consequence, existing algorithms are difficult to apply.We describe an algorithm for this generation problem which runs in expected linear time O(M) if $$\varDelta ^{2+\epsilon } = O(M)$$ Δ 2 + ϵ = O ( M ) for some constant $$\epsilon > 0$$ ϵ > 0 and $$T - \varDelta = \varOmega (T)$$ T - Δ = Ω ( T ) where $$M = \sum _i d_i$$ M = ∑ i d i and $$\varDelta = \max _i d_i$$ Δ = max i d i . Our algorithm applies the switching method of McKay and Wormald [16] to temporal graphs: we first generate a random temporal multigraph and then remove self-loops and duplicated edges with switching operations which rewire the edges in a degree-preserving manner.

In this paper, an integrative fifth-order biological and mental network model is introduced, to demonstrate epigenetics effects in Post-Traumatic Stress Disorder (PTSD), using an adaptive network modeling approach based on temporal-casual networks. The network model assesses DNA methylation dysregulation, on glucocorticoid receptors, and side effects of glucocorticoid receptor hyperreactivity to glucocorticoids in fear processing of individuals with post-traumatic stress disorder. Furthermore, a form of therapy is explored on differently methylated genes. Genes NR3C1 and FKBP5, and their expression were chosen for the demonstration, furthermore, administering MDMA was chosen as a form of therapy. Several simulations were run to analyze and illustrate behavior of the network model. Behaviors for both genes and their expression were tested together and individually.

This study introduces a new metric called “DynamicScore” to evaluate the dynamics of graphs. It can be applied to both vertices and edges. Unlike traditional metrics, DynamicScore not only measures changes in the number of vertices or edges between consecutive time steps, but also takes into account the composition of these sets. To illustrate the possible contributions of this metric, we calculate it for increasing networks of preferential attachment (Barabási-Albert model) and Edge-Markovian graphs. The results improve our understanding of the dynamics inherent in these generated evolving graphs.

In this paper, we introduce spatiotemporal graph $$ k $$ k -means (STG $$k$$ k M), a novel, unsupervised method to cluster vertices within a dynamic network. Drawing inspiration from traditional $$ k $$ k -means, STG $$k$$ k M finds both short-term dynamic clusters and a “long-lived” partitioning of vertices within a network whose topology is evolving over time. We provide an exposition of the algorithm, illuminate its operation on synthetic data, and apply it to detect political parties from a dynamic network of voting data in the United States House of Representatives. One of the main advantages of STGkM is that it has only one required parameter, namely $$ k $$ k ; we therefore include an analysis of the range of this parameter and guidance on selecting its optimal value. We also give certain theoretical guarantees about the correctness of our algorithm.

We derive a differential-integral equation akin to the Hegselmann -Krause model of opinion dynamics [R. Hegselmann and U. Krause, JASSS, vol. 5, 2002], and propose a particle method for solving the equation. Numerical experiments show second-order weak convergence of the method. We also show that our differential-integral equation can equivalently be stated as a system of differential equations. An integration-by-parts argument that would typically yield an energy dissipation inequality in physical problems yields a concentration inequality here, showing that a natural measure of concentration increases monotonically.

The research on biological network evolution and graph growth models, such as the Duplication-Mutation with Random Mutation (DMR) model, enable us to characterize the protein interaction network’s evolutionary dynamics founded on duplication and divergence via mutation in a principled way. The existing approaches to reconstruct historical ancestral graphs for DMR model mainly focus on greedy approaches and results in suboptimal solutions. In this study, we come up with ILP-DMR, a novel Integer Linear Programming (ILP)-based formulation, to reconstruct historical PPI graphs by likelihood maximization over DMR model. We assess the effectiveness of our approach in reconstructing the history of synthetic as well as optimal history of the proteins from the families of bZIP transcription factors. In comparison to the existing techniques, solutions returned by our ILP-DMR have a higher likelihood and are more robust to model mismatch and noise in the data. Solutions extracted by ILP-DMR have a higher likelihood than the existing methods, and our solutions better agree with the biological findings of different studies. Our datasets and code are available at https://github.com/seferlab/dmrhistory .

We propose a method for identifying multiple influential spreaders in complex networks. This method is based on a farthest-first traversal of the network. The spreaders selected by this method satisfy the two criteria of being dispersed as well as influential in their neighborhood. To examine the influence of the spreaders identified by our method, we perform numerical simulations of SIR-based epidemic spread dynamics. For a range of parameter values, we observe that the epidemic size obtained using the spreaders generated by our method as the initial spreaders is at least as large as the epidemic size obtained using hubs as initial spreaders.

We contrast three distinct mathematical approaches to the hard problem of consciousness: quantum consciousness, integrated information theory, and the very large scale dynamical systems simulation of a network of networks. We highlight their features and their associated hypotheses, and we discuss how they are aligned or in conflict. We suggest some challenges for the future theories, in considering how they might apply to the human brain as it develops both cognitive and conscious sophistication, from infancy to adulthood; and how an evolutionary perspective challenges the distinct approaches to aver performance advantages and physiological surrogates for consciousness.