Rumor Diffusion in an Interests-Based Dynamic Social Network

Box 1

Formalizations of the rules of agents.

(1) ∀a (e = Random(EN))→a @₀e ∧  𝑎⋅𝑃𝑙𝑎𝑦(ignorant)

(2) ∀a (∀b (a ⊳_𝑡b ∧b = Random(𝐿𝑖𝑛𝑘_𝑎,𝑡)))→Interact(a,b)

(3) 𝑎∶=𝑅𝑎𝑛𝑑𝑜𝑚(AG) →𝑎⋅𝑄𝑢𝑖𝑡(ignorant) ∧  𝑎⋅𝑃𝑙𝑎𝑦(spreader)  ∧  𝑎⋅𝐼_𝑖∶=1

(4) (I)  ∀a (∀b (Iteract(a,b) ∧ 𝑎↓_𝑡  ignorant ∧  𝑏↓_𝑡  spreader ∧ Random(1) > γ)) ∣ [ω]

    →𝑎⋅𝑄𝑢𝑖𝑡(ignorant) ∧  𝑎⋅𝑃𝑙𝑎𝑦(spreader) ∧  𝑎⋅𝐼_𝑖 = 𝑏⋅𝐼_𝑖^∗τ

    (II) ∀a (∀b (Iteract(a,b) ∧  𝑎↓_𝑡  ignorant ∧  𝑏↓_𝑡 spreader ∧ Random(1)  ≤  γ)) ∣ [ω]

    →𝑎⋅𝑄𝑢𝑖𝑡(ignorant) ∧  𝑎⋅𝑃𝑙𝑎𝑦(spreader)  ∧  𝑎⋅𝐼_𝑖 =  𝑏⋅𝐼_𝑖

(5)  ∀a (𝑎↓_𝑡  spreader) ∣ 𝜇→𝑎⋅𝑄𝑢𝑖𝑡(spreader) ∧  𝑎⋅𝑃𝑙𝑎𝑦(stifler)

(6) ∀a (∀b (Iteract(a,b) ∧  𝑎↓_𝑡  spreader ∧  (𝑏↓_𝑡  spreader ∨  𝑏↓_𝑡  stifler))) ∣ [ε]→𝑎⋅𝑄𝑢𝑖𝑡(spreader) ∧

   𝑎⋅𝑃𝑙𝑎𝑦(stifler)