Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Emergence of Phase Transitions in Complex Contagions

Saurabh Sharma, Ambuj Singh

Abstract

Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold mechanisms based solely on the number of infected neighbors and do not account for the interaction between individual preferences, local social influence, and global sentiment. Moreover, the emergence of virality through phase transitions and tipping points remains poorly characterized. In this paper, we propose a unified propagation cascade model in which notions propagate as high-dimensional vectors in the same feature space as network nodes. Node activations are governed by a unified decision function that integrates propagation affinity, local influence, and global influence. The resulting dynamics induce a stochastic, Markovian cascade process that enables efficient MCMC sampling of propagation outcomes. Using preferential attachment networks, we systematically study spread distributions, incubation dynamics, parameter sensitivity, and phase transition behavior. Our results show that balanced interactions between local reinforcement and global activation are critical for successful cascades and that early-stage growth patterns provide reliable signals of impending phase transitions.

Emergence of Phase Transitions in Complex Contagions

Abstract

Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold mechanisms based solely on the number of infected neighbors and do not account for the interaction between individual preferences, local social influence, and global sentiment. Moreover, the emergence of virality through phase transitions and tipping points remains poorly characterized. In this paper, we propose a unified propagation cascade model in which notions propagate as high-dimensional vectors in the same feature space as network nodes. Node activations are governed by a unified decision function that integrates propagation affinity, local influence, and global influence. The resulting dynamics induce a stochastic, Markovian cascade process that enables efficient MCMC sampling of propagation outcomes. Using preferential attachment networks, we systematically study spread distributions, incubation dynamics, parameter sensitivity, and phase transition behavior. Our results show that balanced interactions between local reinforcement and global activation are critical for successful cascades and that early-stage growth patterns provide reliable signals of impending phase transitions.
Paper Structure (45 sections, 28 equations, 11 figures, 2 tables)

This paper contains 45 sections, 28 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Diffusion of innovations.
  4. Complex contagion and computational models.
  5. Network propagation, label propagation, and diffusion processes.
  6. Network formation and structural models.
  7. Phase transitions and virality in networked systems.
  8. Method
  9. Preliminaries
  10. Unified Propagation of Complex Contagion
  11. Propagation Affinity
  12. Local Influence
  13. Global Influence
  14. Aggregating Influences and Simulating Contagion
  15. Conditions for Local Incubation
  16. ...and 30 more sections

Figures (11)

  • Figure 1: Qualitative illustration of a PA network, $G(1000,2)$ used in our simulations. Node size and color opacity indicate degree and the component along the first spectral embedding vector respectively.
  • Figure 2: (a): Distribution of final cascade sizes across simulation runs, showing a bimodal separation between localized and large-scale cascades. (b): Correlation between average seed-node degree and cascade size, illustrating the influence of core versus peripheral seeding.
  • Figure 3: (a) Temporal evolution of cumulative activated nodes during cascades. (b) Number of newly activated nodes at each time step, highlighting the non-linear phase transition into virality and the tipping point into rapid diffusion.
  • Figure 4: Average time required to reach the viral regime and the network diameter as a function of network size.
  • Figure 5: Effect of the feature affinity weight $\alpha$ on the virality frequency and time to virality.
  • ...and 6 more figures