<｜begin▁of▁sentence｜>### Instruction:
As a museum curator tasked with designing an exhibit around the interconnected stories and historical events from different eras, imagine we have a collection of artifacts, each with a connection to another from a subsequent era, creating a directional, temporal flow of influence. Each connection has a weight, signifying the strength of the relationship between one artifact and the next, akin to a chain of inspiration through time.

For this exhibit layout, we have an initial selection of connections: the artifact from Era 0 influencing one from Era 1 with a weight of 3, then from Era 1 to Era 2 with a weight of 2, from Era 2 to Era 3 with a weight of 1, and finally from Era 3 to Era 4 with a weight of 4. This creates a directed sequence of inspiration or influence from one artifact to another.

In considering the layout and interpretive materials, we want to understand the contextual probability that an artifact from one era, with a certain number of consequential connections, would lead to another artifact with a specific number of incoming influences from predecessor eras. In essence, this is to assess the likelihood that a degree of outgoing influence from one artifact aligns with a degree of ingoing influence on its successor, in a normalized form to factor for the overall pattern in this historical narrative.

Could you contemplate how we might articulate this normalized joint probability, reflecting both the number of outgoing connections from an artifact (out-degree) and the number of times an artifact has been influenced (in-degree), across our dataset of inter-era artifact connections?
### Response:
import networkx as nx

# Create a directed graph
G = nx.DiGraph()
G.add_weighted_edges_from([(0, 1, 3), (1, 2, 2), (2, 3, 1), (3, 4, 4)])

# Use the degree_mixing_dict function
degree_mix_dict = nx.degree_mixing_dict(G, x='out', y='in', weight='weight', normalized=True)

print(degree_mix_dict)
<|EOT|>
