Editing Openai/693343d7-a38c-8012-a67c-11cbed4c0fd9 (section)

=== Extend agent tuple: ===

<syntaxhighlight>A = (S, M, P, C, F, A_c, Ω, θ)

</syntaxhighlight>

where θ are persistent social attributes or embedding vectors used for similarity.

Define network adjacency with affinities:

<syntaxhighlight>W_{i,j}(t) ∈ [0,1]  (weighted directed adjacency)
W_{i,j}(t+1) = g( W_{i,j}(t), Aff(A_i, A_j), interaction_history, τ )

</syntaxhighlight>

Simple discrete dynamics (link formation / rewiring):

<syntaxhighlight>ΔW_{ij} = λ_form · (Aff(A_i,A_j) - W_{ij}) - λ_decay · W_{ij} + η_{ij}(t)
W_{ij} ← clamp(W_{ij} + ΔW_{ij}, 0, 1)

</syntaxhighlight>

Interpretation:
* high Aff → increase connection strength,
* decay and noise terms model forgetting and turnover.