Physics

Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections of all-to-all pair-wise interactions (cliques) and/or group interactions, involving many of their members at once. In this work, focusing on interaction structures represented as simplicial complexes, we present a discrete-time microscopic model of complex contagion for a susceptible-infected-susceptible dynamics. Introducing a particular edge clique cover and a heuristic to find it, the model accounts for the higher-order dynamical correlations among the members of the substructures (cliques/simplices). The analytical computation of the critical point reveals that higher-order correlations are responsible for its dependence on the higher-order couplings. While such dependence eludes any mean-field model, the possibility of a bi-stable region is extended to structured populations.

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and well-understood ensembles of random networks (such as Erdős-Rényi graphs, random geometric graphs, Watts-Strogatz graphs, the configuration model, and preferential attachment networks) are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.

Network optimization has generally been focused on solving network flow problems, but recently there have been investigations into optimizing network characteristics. Optimizing network connectivity to maximize the number of nodes within a given distance to a focal node and then minimizing the number and length of additional connections has not been as thoroughly explored, yet is important in several domains including transportation planning, telecommunications networks, and geospatial analysis. We compare several heuristics to explore this network connectivity optimization problem with the use of random networks, including the introduction of two planar random networks that are useful for spatial network simulation research, and a real-world case study from urban planning and public health. We observe significant variation between nodal characteristics and optimal connections across network types. This result along with the computational costs of the search for optimal solutions highlights the difficulty of finding effective heuristics. A novel genetic algorithm is proposed and we find this optimization heuristic outperforms existing techniques and describe how it can be applied to other combinatorial and dynamic problems.

Hospitals constitute highly interconnected systems that bring into contact an abundance of infectious pathogens and susceptible individuals, thus making infection outbreaks both common and challenging. In recent years, there has been a sharp incidence of antimicrobial-resistance amongst healthcare-associated infections, a situation now considered endemic in many countries. Here we present network-based analyses of a data set capturing the movement of patients harbouring drug-resistant bacteria across three large London hospitals. We show that there are substantial memory effects in the movement of hospital patients colonised with drug-resistant bacteria. Such memory effects break first-order Markovian transitive assumptions and substantially alter the conclusions from the analysis, specifically on node rankings and the evolution of diffusive processes. We capture variable length memory effects by constructing a lumped-state memory network, which we then use to identify overlapping communities of wards. We find that these communities of wards display a quasi-hierarchical structure at different levels of granularity which is consistent with different aspects of patient flows related to hospital locations and medical specialties.

This paper provides the first empirical network analysis of the Argentine interbank money market. Its main topological features are examined applying graph theory, focusing on the unsecured overnight loans settled from 2003 to 2017. The network, where banks are the nodes and the operations between them represent the links, exhibits low density, a higher reciprocity than comparable random graphs, short average distances and its clustering coefficient remains above that of a random network of equal size. Furthermore, the network is prominently disassortative. Its structural metrics experienced significant volatility, in correlation with the economic activity fluctuations and regulatory shifts. Signs of nodes' random-like behavior are detected during contractions. The degree distributions fit better to a Lognormal distribution than to a Poisson or a Power Law. Additionally, different node centrality measures are computed. It is found that a higher centrality enables a node to settle more convenient bilateral interest rates compared to the average market rate, identifying a statistical and economically significant effect by means of a regression analysis. These results constitute a relevant input for systemic risk assessment and provide solid empirical foundations for future theoretical modelling and shock simulations, especially in the context of underdeveloped financial systems.

In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model proposed by Barabasi and Albert: nodes are added to the network connecting preferably to other nodes that are more connected. We also presented models that consider more representative elements from social perspectives, such as the homophily between the vertices or the fitness that each node has to build connections. Furthermore, we showed a version of these models including the Euclidean distance between the nodes as a preferential attachment rule. Our objective is to investigate the basic properties of these networks as distribution of connectivity, degree correlation, shortest path, cluster coefficient and how these characteristics are affected by the preferential attachment rules. Finally, we also provided a comparison of these synthetic networks with real ones. We found that characteristics as homophily, fitness and geographic distance are significant preferential attachment rules to modeling real networks. These rules can change the degree distribution form of these synthetic network models and make them more suitable to model real networks.

In this work we introduce a new nodes attack strategy removing nodes with highest conditional weighted betweenness centrality (CondWBet). We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network in addition to the commonly used binary-topological measure, the largest connected cluster (LCC). We find that the recently proposed conditional betweenness strategy (CondBet) (Nguyen et al. 2019) is the best to fragment the LCC in all cases. Further, we find that the introduced CondWBet strategy is the best to decrease the network efficiency (WEFF) in 3 out of 5 cases. Last, CondWBet is be the most effective strategy to reduce WEFF at the beginning of the removal process whereas the Strength that removes nodes with highest link weights first, shows the highest efficacy in the final phase of the removal process when the network is broken in many small clusters. These last outcomes would suggest that a better attacking strategy could be a combination of the CondWBet and Strength strategies

Echo chambers in online social networks, whereby users' beliefs are reinforced by interactions with like-minded peers and insulation from others' points of view, have been decried as a cause of political polarization. Here, we investigate their role in the debate around the 2016 US elections on Reddit, a fundamental platform for the success of Donald Trump. We identify Trump vs Clinton supporters and reconstruct their political interaction network. We observe a preference for cross-cutting political interactions between the two communities rather than within-group interactions, thus contradicting the echo chamber narrative. Furthermore, these interactions are asymmetrical: Clinton supporters are particularly eager to answer comments by Trump supporters. Beside asymmetric heterophily, users show assortative behavior for activity, and disassortative, asymmetric behavior for popularity. Our findings are tested against a null model of random interactions, by using two different approaches: a network rewiring which preserves the activity of nodes, and a logit regression which takes into account possible confounding factors. Finally, we explore possible socio-demographic implications. Users show a tendency for geographical homophily and a small positive correlation between cross-interactions and voter abstention. Our findings shed light on public opinion formation on social media, calling for a better understanding of the social dynamics at play in this context.

We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed v on a two--dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle, with the addition of a perturbation of amplitude η (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude η . In the static case scenario v=0 where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise η c >0 the system reaches a steady state of complete disorder in the thermodynamic limit, while for η=0 full order is eventually achieved for a system with any number of particles N . Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise ( η>0 ). We show that the finite-size transition noise vanishes with N as η 1D c ??N ?? and η 2D c ??(NlnN) ??/2 in one and two--dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed v>0 , an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude η c >0 that is proportional to v , and that scales approximately as η c ?�v(?�lnv ) ??/2 for v?? . These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.

We investigate the effect of nonlinear redistributive drifts on the dynamics of wealth described by a Fokker-Planck equation for the probability density function P(w,t) of wealth w at time t . We consider (i) a piecewise linear tax, exempting those with wealth below a threshold w 0 , and taxing the excess wealth with given rate, otherwise, and (ii) a power-law tax with exponent α>0 (hence, progressive for α>1 and regressive otherwise). In all cases, the collected amount of wealth is redistributed equally. We analyze how these rules modify the distribution of wealth across the population and, mainly, the inequality level measured through the Gini coefficient G . The introduction of an exemption threshold not always diminishes inequality, depending on the implementation details. Moreover, nonlinearity brings new stylized facts in comparison to the liner case, e.g., negative skewness, bimodal P(w,t) indicating stratification, or a flat shape meaning equality populated wealth layers.