Men who have sex with men (MSM) remain disproportionately affected by HIV, yet optimizing the distribution of pre-exposure prophylaxis (PrEP) in this population remains a major public health challenge. Current PrEP eligibility guidelines and most modelling studies do not incorporate sociodemographic or network-level factors that shape transmission. We present a novel network reconstruction framework that generates MSM sexual contact networks from individual-level behavioral data, incorporating clustering and demographic assortativity by age, race, and sexual activity. Using data from 4667 MSM participants, we reconstructed networks with varying topological properties and simulated HIV transmission over 50 years. Network structure strongly influenced outcomes: assortative by degree networks showed 18

Anxiety and depression are among the most prevalent mental disorders, frequently co-occurring and presenting challenges in diagnosis and treatment. Understanding their underlying cognitive and emotional organization is essential for developing accurate and effective interventions. This study applied a cognitive network science approach to explore semantic and emotional patterns in narratives written by individuals reporting symptoms of anxiety, depression, comorbid symptoms, and no symptoms (asymptomatic). Using co-occurrence and correlation-based estimation methods, networks were constructed with and without stopwords to examine their structural differences. Key analyses included structural properties, emotional balance, and semantic frames of central words to identify group-specific patterns. Distinct cognitive and emotional profiles emerged. Anxiety and depression groups were characterized by denser but fragmented networks, dominated by negative emotional content. Narratives from depression group additionally showed a prominent presence of somatic-related concepts and higher emotional balance, reflecting the co-occurrence of positive and negative concepts within the same semantic structure. The comorbid group combined relatively high density with the lowest emotional balance, indicating greater emotional tension and ambivalent semantic organization. In contrast, the asymptomatic group demonstrated sparser yet more coherently organized and efficient networks, alongside the highest emotional balance, suggesting a more stable and regulated cognitive–emotional profile. These findings demonstrate the utility of cognitive network analysis for capturing differences in semantic and emotional organization associated with anxiety and depressive symptom profiles. By integrating network topology, emotional balance, and semantic framing, this approach offers a nuanced framework for investigating cognitive and emotional processes beyond isolated word use, with potential implications for personalized therapeutic interventions and the monitoring of treatment outcomes.

How do networks of social relationships evolve over time? This study addresses the lack of longitudinal analyses of social networks grounded in mathematical modelling. We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite shifts in individual relationships, the macroscopic structure of the network remains stable, fluctuating within predictable bounds. We link this stability to the concept of equilibrium in statistical physics. Specifically, we show that the probabilities governing link dynamics are stationary over time, and that key network features align with equilibrium predictions. Moreover, the dynamics also satisfy the detailed balance condition. This equilibrium persists despite ongoing turnover, as individuals join, leave, and shift connections. This suggests that equilibrium arises not from specific individuals but from the balancing act of human needs, cognitive limits, and social pressures. Practically, this equilibrium simplifies data collection, supports methods relying on single network snapshots (like Exponential Random Graph Models), and aids in designing interventions for social challenges. Theoretically, it offers insights into collective human behaviour, revealing how emergent properties of complex social systems can be captured by simple mathematical models.

IOTA is a distributed ledger technology that relies on a peer-to-peer (P2P) network for communications. Recently an auto-peering algorithm was proposed to build connections among IOTA peers according to their "Mana" endowment, which is an IOTA internal reputation system. This paper's goal is to detect potential vulnerabilities and evaluate the resilience of the P2P network generated using IOTA auto-peering algorithm against eclipse attacks. In order to do so, we interpret IOTA's auto-peering algorithm as a random network formation model and employ different network metrics to identify cost-efficient partitions of the network. As a result, we present a potential strategy that an attacker can use to eclipse a significant part of the network, providing estimates of costs and potential damage caused by the attack. On the side, we provide an analysis of the properties of IOTA auto-peering network ensemble, as an interesting class of homophile random networks in between 1D lattices and regular Poisson graphs.

Understanding the mindset of people who die by suicide remains a key research challenge. We map conceptual and emotional word–word co-occurrences in 139 genuine suicide notes and in reference word lists, an Emotional Recall Task, from 200 individuals grouped by high/low depression, anxiety, and stress levels on DASS-21. Positive words cover most of the suicide notes’ vocabulary; however, co-occurrences in suicide notes overlap mostly with those produced by individuals with low anxiety (Jaccard index of 0.42 for valence and 0.38 for arousal). We introduce a “words not said” method: It removes every word that corpus A shares with a comparison corpus B and then checks the emotions of “residual” words in A−B. With no leftover emotions, A and B are similar in expressing the same emotions. Simulations indicate this method can classify high/low levels of depression, anxiety and stress with 80% accuracy in a balanced task. After subtracting suicide note words, only the high-anxiety corpus displays no significant residual emotions. Our findings thus pin anxiety as a key latent feature of suicidal psychology and offer an interpretable language-based marker for suicide risk detection.

Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This polarity reshapes how we think about structure and dynamics in complex systems: a negative tie is not simply a missing positive one but a constraint that generates tension, and possibly asymmetry. Across disciplines, from sociology to neuroscience and machine learning, signed networks provide a shared language to formalise duality, balance, and opposition as integral components of system behaviour. This review provides a comprehensive and foundational summary of signed network theory. It formalises the mathematical principles of signed graphs and surveys signed-network-specific measures, including signed degree distributions, clustering, centralities, motifs, and Laplacians. It revisits balance theory, tracing its cognitive and structural formulations and their connections to frustration. Structural aspects of signed networks are examined, analysing key topics such as null models, node embeddings, sign prediction, and community detection. Subsequent sections address dynamical processes on and of signed networks, such as opinion dynamics, contagion models, and data-driven approaches for studying evolving networks. Practical challenges in constructing, inferring and validating signed data from real-world systems are also highlighted, and we offer an overview of currently available datasets. We also address common pitfalls and challenges that arise when modelling or analysing signed data. Overall, this review integrates theoretical foundations, methodological approaches, and cross-domain examples, providing a structured entry point and a reference framework for researchers interested in the study of signed networks in complex systems.

Blockchain-based systems are frequently governed through tokens that grant their holders voting rights over core protocol functions and funds. The centralisation occurring in Decentralised Finance (DeFi) protocols’ token-based voting systems is typically analysed by examining token holdings’ distribution across addresses. In this paper, we expand this perspective by exploring shared token holdings of addresses across multiple DeFi protocols. We construct a Statistically Validated Network (SVN) based on shared governance token holdings among addresses. Using the links within the SVN, we identify influential addresses that shape these connections and conduct a post-hoc analysis to examine their characteristics and behaviour. Our findings reveal persistent influential links over time, predominantly involving addresses associated with institutional actors or smart-contracts, which hold significant fractions of token supplies across the sampled protocols. Finally, we observe that token holding patterns and concentrations tend to shift in with protocol valuations and dollar denominated Total Value Locked.

The macroscale connectome is the network of physical, white-matter tracts between brain areas. The connections are generally weighted and their values interpreted as measures of communication efficacy. In most applications, weights are either assigned based on imaging features-e.g. diffusion parameters-or inferred using statistical models. In reality, the ground-truth weights are unknown, motivating the exploration of alternative edge weighting schemes. Here, we explore a multi-modal, regression-based model that endows reconstructed fiber tracts with directed and signed weights. We find that the model fits observed data well, outperforming a suite of null models. The estimated weights are subject-specific and highly reliable, even when fit using relatively few training samples, and the networks maintain a number of desirable features. In summary, we offer a simple framework for weighting connectome data, demonstrating both its ease of implementation while benchmarking its utility for typical connectome analyses, including graph theoretic modeling and brain-behavior associations.

In this paper, we introduce a rehab–recovery–relapse cycle model to study the interaction between healthy individuals, individuals that might develop substance use disorders (SUD), which for simplicity here we will call susceptible individuals, individuals with SUD, and individuals recovered in a rehab community. We measure the community’s health through a system defined by four non-linear ordinary differential equations in which we include a rehab community. After computing the SUD-free and coexistence equilibrium points, we find the feasibility and stability conditions of an equivalent and reduced system obtained by nondimensionalizing the equations of the original model. We have numerically investigated the importance of the parameter values on the model’s outcome via a one- and two-strain parameter analysis. From the numerical results, we observe that an efficient rehab community can be characterized by (i) a high recovery rate (the individuals stay in that community as little time as possible) and (ii) permanent rehabilitation being preferred at the expense of a low recovery rate.

This study presents a workflow for identifying and characterizing patients with Heart Failure (HF) and multimorbidity utilizing data from Electronic Health Records. Multimorbidity, the co-occurrence of two or more chronic conditions, poses a significant challenge on healthcare systems. Nonetheless, understanding of patients with multimorbidity, including the most common disease interactions, risk factors, and treatment responses, remains limited, particularly for complex and heterogeneous conditions like HF. We conducted a clustering analysis of 3745 HF patients using demographics, comorbidities, laboratory values, and drug prescriptions. Our analysis revealed four distinct clusters with significant differences in multimorbidity profiles showing differential prognostic implications regarding unplanned hospital admissions. These findings underscore the considerable disease heterogeneity within HF patients and emphasize the potential for improved characterization of patient subgroups for clinical risk stratification through the use of EHR data.

As Internet of Things (IoT) technology grows, so does the threat of malware infections. A proposed countermeasure, the use of benevolent"white worms"to combat malicious"black worms", presents unique ethical and practical challenges. This study examines these issues via network epidemiology models and simulations, considering the propagation dynamics of both types of worms in various network topologies. Our findings highlight the critical role of the rate at which white worms activate themselves, relative to the user's system update rate, as well as the impact of the network structure on worm propagation. The results point to the potential of white worms as an effective countermeasure, while underscoring the ethical and practical complexities inherent in their deployment.

Understanding the mindset of people who end their lives by suicide remains a key research challenge. To this aim, we reconstruct conceptual associations and emotional perceptions of 139 authors of genuine suicide notes, i.e., notes written moments before ending one's own life. Our methods are grounded in cognitive network science, text analysis and psychometrics. We introduce a quantitative framework measuring to what extent authors of suicide notes tend to associate emotional words in ways similar to how 200 individuals with high/low levels of depression, anxiety, and stress (on a DASS-21 scale) recall concepts together. In Study 1, we use text analysis to build one co-occurrence network out of suicide notes' texts and six fluency co-occurrence networks out of fluency data from individuals high/low on anxiety/stress/depression levels. We find that emotional word associations in suicide notes reflect mostly conceptual associations produced by low-anxiety individuals. In Study 2, we perform residual emotional profiling, i.e. measuring the emotional intensity of words remaining after removing from fluency networks those words mentioned and connected in the suicide notes' network. We find that only the high-anxiety fluency network displays negligible emotional residuals, indicating the highest overlap - in terms of emotions - between suicide notes' content and the concepts recalled by individuals with high anxiety levels. We discuss how these findings relate to existing psychological literature, along with their potential implications for understanding and quantifying suicidal behavior.

Polarization, or a division into mutually hostile groups, is a common feature of social systems. It is studied in Structural Balance Theory in terms of semicycles in signed networks. However, enumerating semicycles is computationally expensive, so approximations are often needed. Here we introduce the Multiscale Semiwalk Balance approach for measuring the degree of balance (DoB) in (un)directed, (un)weighted signed networks by approximating semicycles with closed semiwalks. It allows selecting the resolution of analysis appropriate for assessing DoB motivated by the Locality Principle, which posits that patterns in shorter cycles are more important than in longer ones. Our approach overcomes several limitations affecting walk-based approximations and provides methods for assessing DoB at various scales, from graphs to individual nodes, and for clustering signed networks. We demonstrate its effectiveness by applying it to real-world social systems, which leads to explainable results for networks with expected patterns (polarization in the US Congress) and a more nuanced perspective for other systems. Our work may facilitate studying polarization and structural balance in a variety of contexts and at multiple scales.

In the healthcare sector, resorting to big data and advanced analytics is a great advantage when dealing with complex groups of patients in terms of comorbidities, representing a significant step towards personalized targeting. In this work, we focus on understanding key features and clinical pathways of patients with multimorbidity suffering from Dementia. This disease can result from many heterogeneous factors, potentially becoming more prevalent as the population ages. We present a set of methods that allow us to identify medical appointment patterns within a cohort of 1924 patients followed from January 2007 to August 2021 in Hospital da Luz (Lisbon), and to stratify patients into subgroups that exhibit similar patterns of interaction. With Markov Chains, we are able to identify the most prevailing medical appointments attended by Dementia patients, as well as recurring transitions between these. To perform patient stratification, we applied AliClu, a temporal sequence alignment algorithm for clustering longitudinal clinical data, which allowed us to successfully identify patient subgroups with similar medical appointment activity. A feature analysis per cluster obtained allows the identification of distinct patterns and characteristics. This pipeline provides a tool to identify prevailing clinical pathways of medical appointments within the dataset, as well as the most common transitions between medical specialities within Dementia patients. This methodology, alongside demographic and clinical data, has the potential to provide early signalling of the most likely clinical pathways and serve as a support tool for health providers in deciding the best course of treatment, considering a patient as a whole.

The brain’s functional networks can be assessed using imaging techniques like functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). Recent studies have suggested a link between the dynamic functional connectivity (dFC) captured by these two modalities, but the exact relationship between their spatiotemporal organization is still unclear. Since these networks are spatially embedded, a question arises whether the topological features captured can be explained exclusively by the spatial constraints. We investigated the global structure of resting-state EEG and fMRI data, including a spatially informed null model and found that fMRI networks are more modular over time, in comparison to EEG, which captured a less clustered topology. This resulted in overall low similarity values. However, when investigating the community structure beyond spatial constraints, this similarity decreased. We show that even though EEG and fMRI functional connectomes are slightly linked, the two modalities essentially capture different information over time, with most but not all topology being explained by the underlying spatial embedding.

The genomic expression of living organisms is controlled by complex transcriptional regulation. Transcriptional regulatory networks, composed by associations between transcription factors and target genes, are responsible for representing and controlling this gene expression and regulate the response of an organism to environmental changes. In this paper, we extend the study of these systems by applying different community detection algorithms on closely-related yeast transcriptional regulation networks to characterize their topological structure and understand if these methods are able to capture meaningful functional clusters of genes. We start by evaluating the accuracy and efficiency of a large group of algorithms by applying them to benchmark networks with ground-truth communities. We then apply the methods that had the best performance to the yeast networks to analyze the quality of the resulting structures, and then, assess the quality of the retrieved modules from a biological point of view using available annotated species' biological functions. Finally, we apply a multilayer community detection algorithm on multilayer networks, where each layer is an individual yeast network, and use available mappings between nodes of different species to successfully discover communities with genes that belong to different species but have similar biological functions. We conclude that the use of community detection algorithms to functionally characterize the modules of these networks might not be enough, suggesting the need of additional genetic information and possibly the use of alternative strategies to study these complex regulatory networks.

Optimal percolation concerns the identification of the minimum-cost strategy for the destruction of any extensive connected components in a network. Solutions of such a dismantling problem are important for the design of optimal strategies of disease containment based either on immunization or social distancing. Depending on the specific variant of the problem considered, network dismantling is performed via the removal of nodes or edges, and different cost functions are associated to the removal of these microscopic elements. In this paper, we show that network representations in geometric space can be used to solve several variants of the network dismantling problem in a coherent fashion. Once a network is embedded, dismantling is implemented using intuitive geometric strategies. We demonstrate that the approach well suits both Euclidean and hyperbolic network embeddings. Our systematic analysis on synthetic and real networks demonstrates that the performance of embedding-aided techniques is comparable to, if not better than, the one of the best dismantling algorithms currently available on the market.

The macroscale connectome is the network of physical, white-matter tracts between brain areas. The connections are generally weighted and their values interpreted as measures of communication efficacy. In most applications, weights are either assigned based on imaging features–e.g. diffusion parameters–or inferred using statistical models. In reality, the ground-truth weights are unknown, motivating the exploration of alternative edge weighting schemes. Here, we explore a multi-modal (combining diffusion and functional MRI data) regression-based, explanatory model that endows reconstructed fiber tracts with directed and signed weights. Benchmarking this method on Human Connectome Project data, we find that the model fits observed data well, outperforming a suite of null models. The estimated weights are subject-specific and highly reliable, even when fit using relatively few training samples. Next, we analyze the resulting network using graph-theoretic tools from network neuroscience, revealing bilaterally symmetric communities that span cerebral hemispheres. These communities exhibit a clear mapping onto known functional systems. We also study the shortest paths structure of this network, discovering that almost every edge participates in at least one shortest path. We also find evidence of robust asymmetries in edge weights, that the network reconfigures in response to naturalistic stimuli, and that estimated edge weights differ with age. In summary, we offer a simple framework for weighting connectome data, demonstrating both its ease of implementation while benchmarking its utility for typical connectome analyses, including graph theoretic modeling and brain-behavior associations.

Trust is key to the efficient functioning of any fiat or crypto-currency and so is for the consensus algorithm behind the functioning of blockchain systems. By an arbitrary design choice, Bitcoin and most Proof-of-Work (PoW) blockchains have a limited supply. Once block rewards vanish, only transaction fees will remain as an incentive for miners to partake in the verification process. In this paper, we analyse the impact that miners bargaining over block composition has on consensus in the absence of block rewards: in this situation, competing blocks at the same height may be more attractive to peers by including less transactions (i.e. sharing the mempool). The mining and acceptance of blocks can be modelled as an Ultimatum Game, where miners' strategies represent their fairness sentiment. Extending previous Literature, our study focuses on the effect of the transaction arrival rate on global consensus in the system and whether local consensus is formed under certain assumptions about the strategies of miners. We find that consensus is threatened when the supply of transactions is low and stable consensus only emerges when the amount of unconfirmed transactions remains sufficient. In addition, when miners are set with randomised strategies, it is more difficult for the system to achieve consensus. Our research suggests that transitioning from a block reward incentive to a transaction fee incentive may weaken and even destroy the consensus of PoW-based systems.

Transcriptional regulatory networks are responsible for controlling gene expression. These networks are composed of many interactions between transcription factors and their target genes. Carrying a combinatorial nature that encompasses several regulatory processes, they allow an organism to respond to disturbances that may occur in the surrounding environment. In this work, we study transcriptional regulatory networks of closely related yeast species with the aim of revealing which functions or processes are encoded in the regulatory network topology. The first phase of this work consists of the detection of modules followed by their functional characterization. Here, we unveil the functionality of the species by capturing it in functional modules. In the second phase, we move towards a cross-species analysis where we compare the functional modules of the different species to settle the similarities between them. Lastly, we use a multilayer network approach to combine the genetic information of different species. We seek to identify the functional elements conserved across the different organisms by applying a detection of modules in the multilayer network.