Reliability and efficiency of generalized rumor spreading model on complex social networks

We introduce the generalized rumor spreading model and investigate some properties of this model on different complex social networks. Despite pervious rumor models that both the spreader-spreader ($SS$) and the spreader-stifler ($SR$) interactions have the same rate $\alpha$, we define $\alpha^{(1)}$ and $\alpha^{(2)}$ for $SS$ and $SR$ interactions, respectively. The effect of variation of $\alpha^{(1)}$ and $\alpha^{(2)}$ on the final density of stiflers is investigated. Furthermore, the influence of the topological structure of the network in rumor spreading is studied by analyzing the behavior of several global parameters such as reliability and efficiency. Our results show that while networks with homogeneous connectivity patterns reach a higher reliability, scale-free topologies need a less time to reach a steady state with respect the rumor.

💡 Research Summary

The paper presents a generalized rumor‑spreading model that relaxes a common assumption in classic rumor dynamics: the rates at which a spreader becomes a stifler after meeting another spreader (SS interaction) and after meeting a stifler (SR interaction) are taken to be identical. Instead, the authors introduce two distinct rates, α⁽¹⁾ for SS → RS transitions and α⁽²⁾ for SR → RR transitions. The model also retains the usual spreading rate λ (set to 1 in the analysis) and a forgetting rate δ that allows a spreader to become a stifler without any contact.

Using a mean‑field approach on uncorrelated networks, the authors derive differential equations for the densities of ignorants (Iₖ), spreaders (Sₖ), and stiflers (Rₖ) for each degree class k. By assuming random mixing (P(l|k)=l p(l)/⟨k⟩) the equations simplify, and an auxiliary function φ(t) = ∫₀ᵗ⟨k⟩Sₖ(t′)dt′ is introduced. This leads to an exact expression for the ignorant density Iₖ(t)=Iₖ(0) exp