Reentrant phase transitions in threshold driven contagion on multiplex networks

Abstract

Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a novel theoretical explanation for the observation of large scale contagion in highly connected but heterogeneous networks.

Dynamics of cascades on burstiness-controlled temporal networks

“…This transition is determined by β j dt, the probability of an uninfected neighbour in configuration j becoming infected over an interval dt (see Methods for an explicit calculation). Taken together, W ego and W neigh accurately describe diffusion dynamics over static networks with heterogeneous edge types, such as weighted and multiplex networks 33,34 .…”

“…Threshold dynamics, also known as complex contagion, are used to model the spread of information where infection requires the reinforced influence of at least a certain fraction of neighbours in the egocentric network 29 . Thresholddriven dynamics over static networks have been extensively studied both empirically 30 and theoretically [30][31][32][33][34] , but analysis of their behaviour on temporal networks is so far limited to a small number of empirical studies [35][36][37][38] . Using random reference models of temporal networks, it has been shown that when infection is driven by the fraction of infected neighbours, rather than their absolute number, bursty interactions may lead to deceleration 35,36,38 .…”

Cascading behavior of an extended Watts model on networks

“…For example, some studies have shown that a global cascade can occur more easily when a network is highly clustered [8][9][10] or is positively degree-correlated [11][12][13][14] than when it is not. Other studies have investigated the Watts model on modular networks [11,[15][16][17], temporal networks [18][19][20], and multiplex networks [21][22][23].…”

Dynamics of cascades on burstiness-controlled temporal networks

“…Threshold dynamics, also known as complex contagion, are used to model the spread of information where infection requires the reinforced influence of at least a certain fraction of neighbours in the network [28]. Threshold * samuel.unicomb@gmail.com driven dynamics over static networks have been extensively studied both empirically [29] and theoretically [29][30][31][32][33], but analysis of their behaviour on temporal networks has been limited to a small number of empirical studies [34][35][36][37]. Here we propose an analytical framework to systematically describe the relationship between the diffusion of information and bursty temporal interactions, thus providing the theoretical foundation necessary to uncover the role of burstiness in generic diffusion processes, including simple and complex contagion models of physical, biological and social phenomena.…”

“…This transition is determined by β j dt, the probability of an uninfected neighbour in configuration j becoming infected over an interval dt (see Methods for an explicit calculation). Taken together, W ego and W neigh accurately describe diffusion dynamics over static and heterogeneously distributed edges, such as weighted and multiplex networks [32,33].…”