Empirical temporal networks of face-to-face human interactions

The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented level of details and scale. Wearable sensors, in particular, open up a new window on human mobility and proximity in a variety of indoor environments. Here we review stylized facts on the structural and dynamical properties of empirical networks of human face-to-face proximity, measured in three different real-world contexts: an academic conference, a hospital ward, and a museum exhibition. First, we discuss the structure of the aggregated contact networks, that project out the detailed ordering of contact events while preserving temporal heterogeneities in their weights. We show that the structural properties of aggregated networks highlight important differences and unexpected similarities across contexts, and discuss the additional complexity that arises from attributes that are typically associated with nodes in real-world interaction networks, such as role classes in hospitals. We then consider the empirical data at the finest level of detail, i.e., we consider time-dependent networks of face-to-face proximity between individuals. To gain insights on the effects that causal constraints have on spreading processes, we simulate the dynamics of a simple susceptible-infected model over the empirical time-resolved contact data. We show that the spreading pathways for the epidemic process are strongly affected by the temporal structure of the network data, and that the mere knowledge of static aggregated networks leads to erroneous conclusions about the transmission paths on the corresponding dynamical networks.     

Modelling conflicts with cluster dynamics in networks

We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study the model in its annealed random graph version, on a fixed network, and on a network evolving through the actions. The sizes of actions are distributed with a power-law tail, however, the exponent is non-universal and depends on the frequency of actions and sparseness of the available connections between units. Allowing the network reconstruction over time in a self-organized manner, e.g., by adding the links based on previous liaisons between units, we find that the power-law exponent depends on the evolution time of the network. Its lower limit is given by the universal value 5/2, derived analytically for the case of random fragmentation processes. In the temporal patterns behind the size of actions we find long-range correlations in the time series of the number of clusters and the non-trivial distribution of time that a unit waits between two actions. In the case of an evolving network the distribution develops a power-law tail, indicating that through repeated actions, the system develops an internal structure with a hierarchy of units.     

Modelling of weighted evolving networks with community structures

Many social and biological networks consist of communities–groups of nodes within which links are dense but among which links are sparse. It turns out that most of these networks are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the link weights among their nodes. Recently, there are considerable interests in the study of properties as well as modelling of such networks with community structures. To our knowledge, however, no study of any weighted network model with such a community structure has been presented in the literature to date. In this paper, we propose a weighted evolving network model with a community structure. The new network model is based on the inner-community and inter-community preferential attachments and preferential strengthening mechanism. Simulation results indicate that this network model indeed reflect the intrinsic community structure, with various power-law distributions of the node degrees, link weights, and node strengths.     

Epidemic variability in hierarchical geographical networks with human activity patterns

Recently, some studies have revealed that non-Poissonian statistics of human behaviors stem from the hierarchical geographical network structure. On this view, we focus on epidemic spreading in the hierarchical geographical networks and study how two distinct contact patterns (i.e., homogeneous time delay (HOTD) and heterogeneous time delay (HETD) associated with geographical distance) influence the spreading speed and the variability of outbreaks. We find that, compared with HOTD and null model, correlations between time delay and network hierarchy in HETD remarkably slow down epidemic spreading and result in an upward cascading multi-modal phenomenon. Proportionately, the variability of outbreaks in HETD has the lower value, but several comparable peaks for a long time, which makes the long-term prediction of epidemic spreading hard. When a seed (i.e., the initial infected node) is from the high layers of networks, epidemic spreading is remarkably promoted. Interestingly, distinct trends of variabilities in two contact patterns emerge: high-layer seeds in HOTD result in the lower variabilities, the case of HETD is opposite. More importantly, the variabilities of high-layer seeds in HETD are much greater than that in HOTD, which implies the unpredictability of epidemic spreading in hierarchical geographical networks.     

Sequences in neural networks with temporal association

We solve the dynamics of the strongly diluted version of a model recently proposed by Herz et al. to store sequences of patterns with spatio-temporal retrieval properties. We analyze the spurious sequence solutions and we find the region in the (,T) plane where the only relevant attractors are the learnt cycles.     

Burstiness and spreading on temporal networks

We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events take place, a property that tends to be affected by the bulk of the distributions and not only by their tail, as usually considered in the literature. We show that a detailed modeling of the temporal patterns observed in complex networks can change dramatically the properties of a spreading process, such as the ergodicity of a random walk process or the persistence of an epidemic.     

Advances in dynamic temporal networks: Understanding the temporal dynamics of complex adaptive networks

Complex networks have been extensively studied in the past 15 years and with increasing details. However, research on the temporal dynamics of complex networks is largely a new territory yet to map out. The present volume presents a collection of papers dealing with various aspects of the problem and this editorial introduces the field as well as the papers.     

Modelling of discrete-time SIS models with awareness interactions on degree-uncorrelated networks

Many epidemic models ignored the impact of awareness on epidemics in a population, though it is not the case from the real viewpoints. In this paper, a discrete-time SIS model with awareness interactions on degree-uncorrelated networks is considered. We study three kinds of awareness, including local awareness and global awareness which are originated from the epidemic-dependent information, and individual awareness which is epidemic-independent and determined by the individual information. We demonstrate analytically that awareness of the epidemic-dependent information cannot change the epidemic threshold regardless of the global or local spreading information. In contrast, epidemic-independent awareness to individual information increases the epidemic threshold in finite scale-free networks, but cannot halt the absence of epidemic threshold in an infinite scale-free network. By numerical simulations, we find that local awareness has a stronger impact on epidemic prevalence than global awareness. Our findings explore the effects of various types of awareness on epidemic spreading and address their roles in the epidemic control.     

The coevolution of individual economic characteristics and socioeconomic networks

The dynamics of individual characteristics of economic agents is modeled with the link structure influenced by this dynamics: links between agents with similar characteristics are more stable than those between agents with vastly different characteristics. A simple scaling law describes the number of distinct surviving characteristic realizations as a function of the number of agents and the number of possible distinct characteristics realizations. With the chosen specification, the investigated properties do not essentially differ from those found for analogous sociophysics models with a fixed network structure.     

Neural networks with low activity levels

We present a numerical study of a neural network model with a low level of activity. Our findings confirm a previous replica-symmetric mean-field analysis which predicts a much higher storage capacity compared with the standard Hopfield model. Indeed our estimate of the critical storage ratio of the model lies above that yielded analytically. We also obtain good agreement with an analytical investigation of the dynamics of the model.     

Modelling the air transport with complex networks: A short review

Air transport is a key infrastructure of modern societies. In this paper we review some recent approaches to air transport, which make extensive use of theory of complex networks. We discuss possible networks that can be defined for the air transport and we focus our attention to networks of airports connected by flights. We review several papers investigating the topology of these networks and their dynamics for time scales ranging from years to intraday intervals, and consider also the resilience properties of air networks to extreme events. Finally we discuss the results of some recent papers investigating the dynamics on air transport network, with emphasis on passengers traveling in the network and epidemic spreading.     

Global stability of a susceptible-infected-susceptible epidemic model on networks with individual awareness

Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible(SIS) epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results.     

Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities

Despite recent advances in the study of temporal networks, the analysis of time-stampednetwork data is still a fundamental challenge. In particular, recent studies have shownthat correlations in the ordering of links crucially alter causaltopologies of temporal networks, thus invalidating analyses based on static,time-aggregated representations of time-stamped data. These findings not only highlight animportant dimension of complexity in temporal networks, but also call for newnetwork-analytic methods suitable to analyze complex systems with time-varying topologies.Addressing this open challenge, here we introduce a novel framework for the study ofpath-based centralities in temporal networks. Studying betweenness,closeness and reach centrality, we first show than an application of these measures totime-aggregated, static representations of temporal networks yields misleading resultsabout the actual importance of nodes. To overcome this problem, we define path-basedcentralities in higher-order aggregate networks, a recently proposedgeneralization of the commonly used static representation of time-stamped data. Using dataon six empirical temporal networks, we show that the resulting higher-order measuresbetter capture the true, temporal centralities of nodes. Our resultsdemonstrate that higher-order aggregate networks constitute a powerful abstraction, withbroad perspectives for the design of new, computationally efficient data mining techniquesfor time-stamped relational data.     

Approaching human language with complex networks

The interest in modeling and analyzing human language with complex networks is on the rise in recent years and a considerable body of research in this area has already been accumulated. We survey three major lines of linguistic research from the complex network approach: 1) characterization of human language as a multi-level system with complex network analysis; 2) linguistic typological research with the application of linguistic networks and their quantitative measures; and 3) relationships between the system-level complexity of human language (determined by the topology of linguistic networks) and microscopic linguistic (e.g., syntactic) features (as the traditional concern of linguistics). We show that the models and quantitative tools of complex networks, when exploited properly, can constitute an operational methodology for linguistic inquiry, which contributes to the understanding of human language and the development of linguistics. We conclude our review with suggestions for future linguistic research from the complex network approach: 1) relationships between the system-level complexity of human language and microscopic linguistic features; 2) expansion of research scope from the global properties to other levels of granularity of linguistic networks; and 3) combination of linguistic network analysis with other quantitative studies of language (such as quantitative linguistics).     

Modelling of electromagnetic wave interactions with the human body

Electromagnetic modelling plays a more and more important role in the study of complex systems involving Maxwell phenomena, such as the interactions of radiowaves with the human body. Simulation then becomes a credible means in decision making, related to the engineering of complex electromagnetic systems. To increase confidence in the models with respect to reality, validation and uncertainty estimation methods are needed. The different dimensions of model validation are illustrated through dosimetry, i.e., quantification of human exposure to electromagnetic waves. To cite this article: M.-F. Wong, J. Wiart, C. R. Physique 6 (2005).     

Resilience of public transport networks against attacks

The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to targeted attacks. In recent studies of public transport networks of fourteen major cities of the world it was shown that these systems when represented by appropriate graphs may exhibit scale-free behavior [Physica A 380, 585 (2007); Eur. Phys. J. B 68, 261 (2009)]. Our present analysis focuses on the effects that defunct or removed nodes have on the properties of public transport networks. Simulating different directed attack strategies, we derive vulnerability criteria that result in minimal strategies with high impact on these systems.     

Measuring asymmetric temporal interdependencies in simulated and biological networks

We use a newly developed metric to characterize asymmetric temporal interdependencies in networks of coupled dynamical elements. We studied the formation of temporal ordering in a system of coupled Rossler oscillators for different connectivity ratios and network topologies and also applied the metric to investigate the functional structure of a biological network (cerebral ganglia of Helix snail). In the former example we show how the local ordering evolves to the global one as a function of structural parameters of the network, while in the latter we show spontaneous emergence of functional interdependence between two groups of electrodes.     

Threshold model of cascades in empirical temporal networks

Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. In many cases, bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work we propose an extension of Watts’s classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to thresholds in the fraction of contacts, we also investigate the number of contacts within the time window as a basis for influence. To elucidate the model’s behavior, we run the model on real and randomized empirical contact datasets.