<｜begin▁of▁sentence｜>### Instruction:
Imagine you're working on a new animated short that explores the complex web of social interactions within a fantastical city. You want to visually represent the city's social network using a dynamic map that mirrors these interactions. The five main characters in your story represent the nodes of this network, and you want to craft a scene that depicts the randomness of their relationships.

For this creative endeavor, you decide to construct a magical map using the concept of a Random Dot Product Graph (RDPG). Each character has their own unique influence, which we'll portray through latent positions that you'll determine by drawing inspiration from the whimsical characteristics of a 2-dimensional Dirichlet distribution. 

Your first task is to animate a simple and clear version of this map. Each relationship between the characters will either exist or not—a binary visual, with no self-connections to avoid any visual clutter of the character interacting with themselves.

Next, you want to add a layer of complexity to this animated map: the strength of the relationships will be represented by varying brightness or thickness of the lines. To achieve this effect, you'll use weights derived from a mystical source, symbolized by a Poisson distribution with an average influx of magical energy quantified by λ, which equals 2.

As you storyboard this concept, keep in mind the practical tools at your disposal. For the technical realization of your vision, you could use NetworkX, a powerful Python library well-suited for the manipulation and study of the structure, dynamics, and functions of complex networks.
### Response:
import numpy as np
from graspologic.simulations import rdpg

np.random.seed(1)

# Generate random latent positions using a 2-dimensional Dirichlet distribution.
X = np.random.dirichlet([1, 1], size=5)

# Sample a binary RDPG using sampled latent positions.
A = rdpg(X, loops=False)

# Sample a weighted RDPG with Poisson(2) weight distribution
wt = np.random.poisson
wtargs = {'lam': 2}
A_weighted = rdpg(X, loops=False, wt=wt, wtargs=wtargs)
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