Rumor Diffusion in an Interests-Based Dynamic Social Network

Box 3

Formalizations of the social network’s rules.

(1) ∀a (𝑏∶=𝑅𝑎𝑛𝑑𝑜𝑚(𝐴𝐺)  ∧  𝑎⋫_𝑡b ∧  𝑝_𝑖𝑗>  Random(1))→𝑎⋅𝐶𝑟𝑒𝑎𝑡𝑒(𝑎,𝑏)  ∧  l ∶=(𝑎,𝑏)  ∧  𝑙⋅𝑆_𝑖𝑗∶=1

(2) ∀a (∀b (𝑎⊳_𝑡b ∧^~Iteract(a,b) ∧l ∶= (a,b)))→𝑙⋅𝑆_𝑖𝑗∶= 𝑒^−𝜅∗𝑙⋅𝑆_𝑖𝑗

(3) ∀a (∀b (𝑎⊳_𝑡b  ∧  l ∶= (a,b)  ∧  𝑙⋅𝑆_𝑖𝑗  <λ))→Delete(a,b)