Source-linked AI summary
Information spreading on dynamic social networks
Chuang Liu, Zi-Ke Zhang
TL;DR
The paper addresses how information spreading is affected by changing social-network structure, rather than fixed contacts alone. It introduces Fermi-function link rewiring in an SIR model and finds broader, faster spreading when rewiring favors susceptible nodes with more susceptible neighbors. The results also indicate that early spreading dynamics strongly shape whether diffusion dies out or reaches a finite population fraction.
Problem
Prior work mainly examined spreading on static networks, although real social interactions change and information has features distinct from disease infection.
Method
The paper combines an SIR model with fixed recovery time T = 1 and Fermi-function rewiring toward susceptible second-order neighbors selected by susceptible-neighbor payoff.
Results
Broader and faster spreading occurs for β > 0, while cascade distributions on scale-free networks show separated small- and large-size regimes with nearly no cascades of size 10 to 4000 for β = 2.
Takeaways & Limitations
The initial spreading steps are important: informing nodes with more susceptible neighbors helps information reach a finite population fraction quickly.
Takeaways & Limitations
The model does not evaluate temporal communication patterns such as burst activity, which the authors identify as future work.
Abstract
from arXiv · showhide
Nowadays, information spreading on social networks has triggered an explosive attention in various disciplines. Most of previous works in this area mainly focus on discussing the effects of spreading probability or immunization strategy on static networks. However, in real systems, the peer-to-peer network structure changes constantly according to frequently social activities of users. In order to capture this dynamical property and study its impact on information spreading, in this paper, a link rewiring strategy based on the Fermi function is introduced. In the present model, the informed individuals tend to break old links and reconnect to their second-order friends with more uninformed neighbors. Simulation results on the susceptible-infected-recovered (\textit{SIR}) model with fixed recovery time $T=1$ indicate that the information would spread more faster and broader with the proposed rewiring strategy. Extensive analyses of the information cascade size distribution show that the spreading process of the initial steps plays a very important role, that is to say, the information will spread out if it is still survival at the beginning time. The proposed model may shed some light on the in-depth understanding of information spreading on dynamical social networks.
1. Introduction
Prior work largely studied information and epidemic spreading on static networks, although real social interactions change over time. This paper proposes payoff-based Fermi rewiring and reports faster, broader information spreading than on static networks.
- Research gap: Static-network studies overlook that online interactions change as people communicate and form new relationships.Dynamic contact patterns motivate studying how rewiring affects spreading.
- Related work: Adaptive rewiring models typically suppress epidemic spreading by isolating infected individuals and reducing susceptible-infected interactions.Earlier models generally have susceptible individuals avoid infected contacts.
- Research gap: Information spreading differs from disease infection through features including time decay, tie strength, information content, memory, social reinforcement, and non-redundant contacts.These differences motivate a rewiring model designed specifically for information spreading.
- Proposed approach: The proposed model rewires informed individuals toward susceptible second-order neighbors selected through payoff comparison using a Fermi function.The model differs from adaptive disease-spreading models by directing links toward susceptible individuals with more susceptible neighbors.
- Main findings: Simulations report broader and faster spreading on dynamic networks than on static networks, with scale-free networks exhibiting either rapid die-out or diffusion into a finite population fraction.The scale-free result is described as two prevalence regimes.
2. Model
The model uses an SIR process with fixed recovery time T = 1 and dynamically rewires links from informed nodes toward susceptible second-order neighbors. Rewiring probability follows a generalized Fermi function based on the susceptible-neighbor payoffs of candidate nodes.
- SIR process: The SIR model uses S, I, and R states, with one randomly selected informed seed and spreading rate λ across S-I links.Active informed nodes transmit information, while recovered nodes retain it without transmitting further.
- Rewiring rule: Each informed node can rewire a link from a connected susceptible node to a randomly chosen susceptible second-order neighbor with probability p_f.The rewiring strategy changes network structure to support faster information transmission.
- Payoff: Candidate nodes are compared by payoff, defined as the number of susceptible neighbors, because higher-payoff individuals are considered more information hungry.The selected candidate is chosen from a local second-order neighborhood rather than the entire social system.
- Fermi selection: The generalized Fermi parameter β controls responsiveness to payoff differences, with β = 0 corresponding to random rewiring.Positive β favors higher-payoff candidates, while negative β favors lower-payoff candidates.
3. Results & Analysis
Across four network structures, positive-payoff rewiring generally broadens and accelerates information spreading, while its effects depend on network topology and spreading rate. Cascade distributions and parameter sweeps show that early survival and the sign of β strongly shape final reach.
- Experimental setup: The experiments use regular, random, small-world, and scale-free networks with N = 10000 and average degree ⟨k⟩ = 6.Results are averaged over 10000 independent realizations.
- Spreading dynamics: β = 2 produces broader spreading than β = 0, β = −2, and the static baseline across the observed networks.Positive β rewires links toward susceptible nodes with more susceptible neighbors, whereas negative β causes spreading to die quickly.
- Spreading dynamics: Scale-free networks spread information faster and more broadly than the other network types, reflecting the role of heterogeneous hub connectivity.The ordering of recovered-node counts is random > small-world > regular.
- Cascade distributions: Cascade sizes show a small-size power-law regime and a large-size regime, with β > 0 producing more large cascades for the same network structure.For scale-free networks with β = 2, cascades between sizes 10 and 4000 are nearly absent, separating rapid extinction from high-level spreading.
- Dependence on λ: For small λ, positive β can sharply increase final pr and lower the apparent critical spreading rate, while negative β inhibits spreading on scale-free networks.At large λ, nearly all individuals enter the recovered state.
- Dependence on β: On scale-free networks, pr is around 1% for β < 0 but around 23% for β > 0, with a sharp transition near β = 0.This indicates that the sign of β matters more than its precise positive or negative magnitude in the reported regime.
4. Discussion
Positive β makes information spreading broader and faster by preferentially connecting informed individuals to susceptible nodes with more susceptible neighbors. This effect is linked to early access to highly connected nodes, while negative β can quickly suppress spreading.
- 4. Discussion: Positive β induces broader and faster information spreading, especially when nodes with more susceptible neighbors are informed at the beginning.The results on four representative networks support this early-stage mechanism.
- 4. Discussion: The rewiring strategy makes nodes with more susceptible neighbors more likely to become informed, helping information spread through them.For β > 0, the spreading pattern on scale-free networks becomes more hierarchical, reaching large-degree nodes first.
- 4. Discussion: Negative β reconnects informed individuals to susceptible nodes with fewer susceptible neighbors, leading to quick annihilation of the spreading.This contrasts with the positive-payoff trend that favors susceptible nodes able to transmit information onward.
- 4. Discussion: Figure 8 compares the average number of susceptible neighbors of informed individuals across four network types and four rewiring methods at λ = 0.2.The methods are static, β = 0, β = 2, and β = −2, averaged over 10^4 independent realizations.
5. Conclusion
The paper proposes a dynamic SIR-based information-spreading model with Fermi-function link rewiring. Simulations indicate that positive β broadens and accelerates spreading, while early survival is decisive and temporal communication patterns remain for future study.
- 5. Conclusion: The model combines SIR information spreading with link rewiring based on a generalized Fermi function and fixed recovery time T = 1.Rewiring depends on payoff comparisons between selected uninformed individuals.
- 5. Conclusion: Positive β produces broader and faster spreading because individuals with more uninformed neighbors are more likely to be informed early.These uninformed hubs can spread information into a finite population fraction quickly.
- 5. Conclusion: Cascade-size analysis indicates that the initial spreading steps are critical: information can reach a finite fraction of the population if it survives the beginning.The conclusion identifies early survival as a key condition for large spreading cascades.
- 5. Conclusion: Temporal patterns such as burst activity should be studied in future evaluations of the rewiring strategy.The paper identifies human communication patterns as important for information diffusion but does not evaluate these temporal patterns here.