x+1 is a list

Lets build graphs from functions. By graph, I don't mean graphic, by graph I mean the actual data structure.

For this purpose, imagine the following. I will grab a subset of a domain in R, namely D, for this subset I will create N equidistant samples, this samples are going to be the nodes of my graph. The nodes of my graph are going to be connected in the following way.

given $$f(x):D\to D^{\prime }$$ with $$D^{\prime }\subseteq D$$, we build a graph with an adjacency matrix defined by $$A_{ij}$$ the domain is divided in N intervals forming the enumerable finite set $$min(D)+i\cdot h|i\in [0,N-1]\text{and}h:=\frac{max(D)-min(D)}{N}$$ where each element is denoted by $$x_i$$ respectively the graph contains N nodes $$A_{ij}=1⟺\text{argmin}{L}_1(f(x_i),x_{j^{\prime }})=j$$

  
    def build_domain(min_d: float, max_d: float, N: int): return np.linspace(min_d, max_d, N)

    def closest(fx, D: np.ndarray) -> int: return np.argmin(np.abs(fx-D))

    def build_graph(min_d: float, max_d: float, N: int, fn: Callable[[float], float]) -> nx.Graph:
        D = build_domain(min_d, max_d, N)
        G = nx.Graph()
        for i, x in enumerate(D): G.add_node(i, x=x)
        for i, x in enumerate(D):
            if i == N-1: break
            G.add_edge(i, closest(fn(x), D))
        return G
  

with this setting $$f(x)=x+1$$ gives birth to a list