Temporal percolation in activity driven networks

We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity driven network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework based on a mapping to hidden variables networks, we provide expressions for the percolation time marking the onset of a giant connected component in the integrated network. In particular, we consider both the generating function formalism, valid for degree uncorrelated networks, and the general case of networks with degree correlations. We discuss the different limits of the two approach, indicating the parameter regions where the correlated threshold collapses onto the uncorrelated case. Our analytical prediction are confirmed by numerical simulations of the model. The temporal percolation concept can be fruitfully applied to study epidemic spreading on temporal networks. We show in particular how the susceptible-infected- removed model on an activity driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process. This mapping allows to obtain addition information on this process, not available for previous approaches

Random walks in non-Poissoinan activity driven temporal networks

The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an inter-event time between consecutive interactions showing a heavy-tailed distribution. In particular, empirical data has shown that the bursty dynamics of temporal networks can have deep consequences on the behavior of the dynamical processes running on top of them. Here, we study the case of random walks, as a paradigm of diffusive processes, unfolding on temporal networks generated by a non-Poissonian activity driven dynamics. We derive analytic expressions for the steady state occupation probability and first passage time distribution in the infinite network size and strong aging limits, showing that the random walk dynamics on non-Markovian networks are fundamentally different from what is observed in Markovian networks. We found a particularly surprising behavior in the limit of diverging average inter-event time, in which the random walker feels the network as homogeneous, even though the activation probability of nodes is heterogeneously distributed. Our results are supported by extensive numerical simulations. We anticipate that our findings may be of interest among the researchers studying non-Markovian dynamics on time-evolving complex topologies.Postprint (published version

Aging and percolation dynamics in a Non-Poissonian temporal network model

We present an exhaustive mathematical analysis of the recently proposed Non-Poissonian Ac- tivity Driven (NoPAD) model [Moinet et al. Phys. Rev. Lett., 114 (2015)], a temporal network model incorporating the empirically observed bursty nature of social interactions. We focus on the aging effects emerging from the Non-Poissonian dynamics of link activation, and on their effects on the topological properties of time-integrated networks, such as the degree distribution. Analytic expressions for the degree distribution of integrated networks as a function of time are derived, ex- ploring both limits of vanishing and strong aging. We also address the percolation process occurring on these temporal networks, by computing the threshold for the emergence of a giant connected component, highlighting the aging dependence. Our analytic predictions are checked by means of extensive numerical simulations of the NoPAD model

Navigability of temporal networks in hyperbolic space

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remain largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio

Model reproduces individual, group and collective dynamics of human contact networks

Empirical data on the dynamics of human face-to-face interactions across a variety of social venues have recently revealed a number of context-independent structural and temporal properties of human contact networks. This universality suggests that some basic mechanisms may be responsible for the unfolding of human interactions in the physical space. Here we discuss a simple model that reproduces the empirical distributions for the individual, group and collective dynamics of face-to-face contact networks. The model describes agents that move randomly in a two-dimensional space and tend to stop when meeting ‘attractive’ peers, and reproduces accurately the empirical distributions.Postprint (author's final draft

Random walks on temporal networks

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis of the temporal patterns characterizing dynamic networks are still recent, so that many questions remain open. Here, we study how random walks, as paradigm of dynamical processes, unfold on temporally evolving networks. To this aim, we use empirical dynamical networks of contacts between individuals, and characterize the fundamental quantities that impact any general process taking place upon them. Furthermore, we introduce different randomizing strategies that allow us to single out the role of the different properties of the empirical networks. We show that the random walk exploration is slower on temporal networks than it is on the aggregate projected network, even when the time is properly rescaled. In particular, we point out that a fundamental role is played by the temporal correlations between consecutive contacts present in the data. Finally, we address the consequences of the intrinsically limited duration of many real world dynamical networks. Considering the fundamental prototypical role of the random walk process, we believe that these results could help to shed light on the behavior of more complex dynamics on temporally evolving networks.Comment: 14 pages, 13 figure

Generalized voter-like models on heterogeneous networks

We describe a generalization of the voter model on complex networks that encompasses different sources of degree-related heterogeneity and that is amenable to direct analytical solution by applying the standard methods of heterogeneous mean-field theory. Our formalism allows for a compact description of previously proposed heterogeneous voter-like models, and represents a basic framework within which we can rationalize the effects of heterogeneity in voter-like models, as well as implement novel sources of heterogeneity, not previously considered in the literature

Topological properties of a time-integrated activity driven network

Here we consider the topological properties of the integrated networks emerging from the activity driven model [Perra at al. Sci. Rep. 2, 469 (2012)], a temporal network model recently proposed to explain the power-law degree distribution empirically observed in many real social networks. By means of a mapping to a hidden variables network model, we provide analytical expressions for the main topological properties of the integrated network, depending on the integration time and the distribution of activity potential characterizing the model. The expressions obtained, exacts in some cases, the results of controlled asymptotic expansions in others, are confirmed by means of extensive numerical simulations. Our analytical approach, which highlights the differences of the model with respect to the empirical observations made in real social networks, can be easily extended to deal with improved, more realistic modifications of the activity driven network paradigm

Quantifying echo chamber effects in information spreading over political communication networks

Echo chambers in online social networks, in which users prefer to interact only with ideologically-aligned peers, are believed to facilitate misinformation spreading and contribute to radicalize political discourse. In this paper, we gauge the effects of echo chambers in information spreading phenomena over political communication networks. Mining 12 million Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of the former Brazilian President Dilma Rousseff. We define a continuous {political position} parameter, independent of the network's structure, that allows to quantify the presence of echo chambers in the strongly connected component of the network, reflected in two well-separated communities of similar sizes with opposite views of the impeachment process. By means of simple spreading models, we show that the capability of users in propagating the content they produce, measured by the associated spreadability, strongly depends on their attitude. Users expressing pro-impeachment sentiments are capable to transmit information, on average, to a larger audience than users expressing anti-impeachment sentiments. Furthermore, the users' spreadability is correlated to the diversity, in terms of political position, of the audience reached. Our method can be exploited to identify the presence of echo chambers and their effects across different contexts and shed light upon the mechanisms allowing to break echo chambers.Comment: 9 pages, 4 figures. Supplementary Information available as ancillary fil