Social contagion on higher-order structures

Barrat, Alain; de Arruda, Guilherme Ferraz; Iacopini, Iacopo; Moreno, Yamir

doi:10.48550/arxiv.2103.03709

Cited by 2 publications

(2 citation statements)

References 45 publications

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“…Interestingly, if the infection rate associated to the higher-order interactions is high enough, this leads to the emergence of new collective behavior, making the transition from the healthy to the endemic phase explosive, and giving rise to metastable states. This result, obtained analytically by a mean-field analysis and confirmed by numerical simulations [23,24], has also been replicated under different modeling frameworks, such as the microscopic Markov chain approach and the generalised link equation [25,26], and on different higher-order representations, such as hypergraphs [27][28][29]. The disruptive presence of higher-order interactions is not limited to contagion dynamics, as new collective behavior has also been observed in the case of synchronization phenomena [30][31][32][33], random walk [34,35], consensus [36,37], ecological [38,39] and evolutionary dynamics [40] when extended beyond simple dyadic ties.…”

Section: Introductionsupporting

confidence: 67%

Simplicial contagion in temporal higher-order networks

Chowdhary,

Kumar,

Cencetti

et al. 2021

Preprint

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Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly describe social contagion, where individuals acquire new norms or ideas after simultaneous exposure to multiple sources of infections. Simplicial contagion has been proposed as an alternative framework where simplices are used to encode group interactions of any order. The presence of higher-order interactions leads to explosive epidemic transitions and bistability which cannot be obtained when only dyadic ties are considered. In particular, critical mass effects can emerge even for infectivity values below the standard pairwise epidemic threshold, where the size of the initial seed of infectious nodes determines whether the system would eventually fall in the endemic or the healthy state. Here we extend simplicial contagion to timevarying networks, where pairwise and higher-order simplices can be created or destroyed over time. By following a microscopic Markov chain approach, we find that the same seed of infectious nodes might or might not lead to an endemic stationary state, depending on the temporal properties of the underlying network structure, and show that persistent temporal interactions anticipate the onset of the endemic state in finite-size systems. We characterize this behavior on higher-order networks with a prescribed temporal correlation between consecutive interactions and also on heterogeneous simplicial complexes, showing that temporality again limits the effect of higher-order spreading, but in a less pronounced way than for homogeneous structures. Our work suggests the importance of incorporating temporality, a realistic feature of many real-world systems, into the investigation of dynamical processes beyond pairwise interactions.

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Section: Introductionsupporting

confidence: 67%

Simplicial contagion in temporal higher-order networks

Chowdhary,

Kumar,

Cencetti

et al. 2021

Preprint

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“…The analytical approaches derived so far have confirmed the rich phenomenology emerging from the contagion dynamics, characterized by discontinuous phase transitions, bistability and critical mass effects [37,[46][47][48][49][50]. Most approaches follow a heterogeneous mean-field (HMF) framework in which nodes are divided into hyperdegree classes.…”

Section: Introductionmentioning

confidence: 88%

Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

St‐Onge¹,

Iacopini²,

Latora³

et al. 2021

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Several biological and social contagion phenomena, such as superspreading events or social reinforcement, are the results of multi-body interactions, for which hypergraphs offer a natural mathematical description. In this paper, we develop a novel mathematical framework based on approximate master equations to study contagions on random hypergraphs with a heterogeneous structure, both in terms of group size (hyperedge cardinality) and of membership of nodes to groups (hyperdegree). The characterization of the inner dynamics of groups provides an accurate description of the contagion process, without losing the analytical tractability. Using a contagion model where multi-body interactions are mapped onto a nonlinear infection rate, our two main results show how large groups are influential, in the sense that they drive both the early spread of a contagion and its endemic state (i.e., its stationary state). First, we provide a detailed characterization of the phase transition, which can be continuous or discontinuous with a bistable regime, and derive analytical expressions for the critical and tricritical points. We find that large values of the third moment of the membership distribution suppress the emergence of a discontinuous phase transition. Furthermore, the combination of heterogeneous group sizes and nonlinear contagion facilitates the onset of a mesoscopic localization phase, where contagion is sustained only by the largest groups, thereby inhibiting bistability as well. Second, we formulate a simple problem of optimal seeding for hypergraph contagions to compare two strategies: tuning the allocation of seeds according to either node individual properties or according to group properties. We find that, when the contagion is sufficiently nonlinear, groups are more effective seeds of contagion than individual nodes.

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Social contagion on higher-order structures

Cited by 2 publications

References 45 publications

Simplicial contagion in temporal higher-order networks

Simplicial contagion in temporal higher-order networks

Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

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