Investigations on graph-theoretical constructions in Homotopy type theory

{-# OPTIONS --without-K --exact-split #-}
module lib.graph-definitions.Graph
  where
  open import foundations.Core

  record
    Graph (ℓ : Level)
      : Type (lsuc ℓ)
    where
    constructor graph
    field
      Node : Type ℓ
      Edge : Node → Node → Type ℓ
      Node-is-set : Node is-set
      Edge-is-set : (x y : Node) → (Edge x y) is-set

  open Graph

  module _ {ℓ : Level} (G : Graph ℓ) {x y : Node G}
    where

    source : Edge G x y → Node G
    source _ = x

    target : Edge G x y → Node G
    target _ = y

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