Network models

(Full abstract in PDF) Higher-order networks encode more information than pairwise interactions: for example, some metabolic reactions can only take place if three or more reactants are present, but this information would not be captured by pairwise interactions.However, this modeling flexibility comes at a cost: new data needs to be adequately recorded, and new analytical andcomputational tools need to be developed. Moreover, the complexity and computational cost of these tools increaseexponentially as larger group interactions are considered. It is therefore crucial to understand under which conditionshigher-order representations need to be favored over classical pairwise ones.Here [2], we propose a principled approach to optimally compress systems with higher-order interactions—accounting for the complexity of the data and the complexity of the model. Specifically, we determine an optimal order of interactions up to which interactions need be considered to obtain a functionally optimal representation of the system—larger orders can be safely discarded.Formally, we do so by generalizing the concept of network density matrix [3] to account for higher-order diffusivedynamics with the multiorder Laplacian [4] and calculate a (modified) message length corresponding to each order.By minimizing this message length, in the spirit of the original minimum message length principle, we find the optimalcompression of the data. We refer to this procedure as functional reduction. A higher-order network is fully reducible—to a pairwise network—if the optimal order is 1, while its reducibility decreases for increasing optimal orders. We demonstrate the validity of our method by performing an extensive analysis of synthetic networks and investigate the functional reducibility of a broad spectrum of real-world higher-order systems.

While homophily---the tendency to link with similar others---may nurture a sense of belonging and shared values, it can also hinder diversity and widen inequalities. Here, we unravel this trade-off analytically, revealing homophily traps for minority groups: scenarios where increased homophilic interaction among minorities negatively affects their structural opportunities within a network. We demonstrate that homophily traps arise when minority size falls below 25% of a network, at which point homophily comes at the expense of lower structural visibility for the minority group. Our work reveals that social groups require a critical size to benefit from homophily without incurring structural costs, providing insights into core processes underlying the emergence of group inequality in networks.

Uncovering the community structure within complex networks is key to understanding their functional units, dynamics, and organizational patterns. However, popular community detection approaches like modularity optimization are NP-hard and sensitive to initial conditions. The KDA, based on the Markov Influence Graph (MIG) framework, offers a deterministic, polynomial-time solution. Currently, both the KDA algorithm and the fundamental analysis of MIGs rely on long-run characteristics of random walkers in discrete time, such that each random walker spends an equal amount of time at each node. In this paper, we extend the model to a continuous time model by allowing for the random walker to spend heterogeneous times at nodes. For example, in a social network, each agent (node) may take varying amounts of time to pass on or process a piece of information (i.e., the random walker), meaning the walker can spend different time durations at different nodes. Through both simulation and empirical applications, we demonstrate that incorporating a time dimension significantly impacts the community structure of a network. Our algorithm offers wide-ranging applications, from social sciences, economics, and finance to the natural sciences, providing a new lens for exploring complex systems.

Human contact networks such as face-to-face interaction, email exchange, and phone communication often display power-law contact duration distributions with potential cutoffs. One class of models associate each contact with a time-independent persistent probability η, leading to an exponentially decaying probability distribution for individual contact durations with a given η. The observed long tail in the marginal distribution is an aggregate effect of the contact persistence distribution ρ(η), which may arise from various factors. Another class of models accounts for self-reinforcement of agents, i.e., “the longer an agent interacts with a group, the less likely it is to leave”. In these models, the contact persistence probability η(t) is a function of the time t, and an increasing η(t) leads to a contact duration distribution that intrinsically decays slower than exponentially. The two classes of models represent two different generative mechanisms: (I) aggregate effect of time homogeneous processes, versus (II) intrinsic time-heterogeneous processes.In this study, we analytically discuss the two model classes and reveal their mathematical relationship. Moreover, we aim to examine whether it is possible to empirically distinguish which mechanism is truly at work, when both mechanisms can produce the same observed contact duration data. This task is non-trivial because it is impossible to distinguish the two mechanisms by controlling the time t and observing the conditional persistence probability. To this end, we analyse two datasets of human-LLM (Large Language Model) conversations where the content of multi-turn interactions between humans and LLMs is recorded, as well as four human face-to-face interaction networks. The survival modeling framework will be used in an attempt to distinguish between the two mechanisms. To this end, Bayesian inference will be used, as it allows for the quantification of evidence for or against the two competing mechanisms.

Due to both international trade and travels as well as climate change, temperate areas in the Americas and in themediterranean basin are now at risk of future significant and recurrent vector-borne epidemics. Meanwhile, mathe-matical modeling of vector-borne diseases progressively acknowledged the interplay between epidemics and human mobility or between epidemics and climate on spatially distributed models due to ever-growing data availability. However, vector-borne disease models encompassing both climate dependence and multi-scale mobility are still missing to accurately forecast vector-borne epidemics in temperate areas. Here we introduce and compare two multiscale reaction-diffusion metapopulation models based on ordinary differential equations which differ in the modeling of human mobility: one integrating it into the force of infection, the other using a diffusion pattern. Both models encompass a tunable time-scale separation between human mobility and the epidemics, short-range vector mobility, human-mediated vector mobility (e.g. vectors in cars), long-range human mobility due to airline traffic and climate dependency in the demographic and epidemiological parameters. Through exhaustive computational analysis, we assess the impact of mobility features on the emergence of epidemics in the two models on synthetic and real-world networks. We show that systems below the epidemics threshold can undergo significant epidemics due to mobility and that the modeling choice of the latter has a dramatic impact on the emergence and magnitude of the epidemics across spatial and temporal scales. We explain analytically the behavior of the force of infection model using perturbation analysis and discuss the comparative relevance of both models. Then, to study the emergence of those disease in temperate areas we will establish risk maps for dengue epidemics in Italy according to several climate change scenarios, based on demographic, mobility and epidemiological data.