<｜begin▁of▁sentence｜>### Instruction:
As a Fitness Instructor who guides individuals in improving their physical health and conditioning through workouts and training sessions, imagine preparing for a workout session with a group of 10 clients at a fitness studio. Each client represents a vertex, and the connection probability of 0.2 signifies the likelihood of forming links between them during a group workout circuit.

Now, let's consider using the "igraph" toolkit's layout algorithms to determine the optimal positions for each client within the studio space based on the Davidson-Harel approach.
### Response:
from igraph import Graph

# Create a simple graph
vertex_count = 10
g = Graph.Erdos_Renyi(n=vertex_count, p=0.2)

# Apply the Davidson-Harel layout algorithm
dh_layout = g.layout_davidson_harel(
    maxiter=1000,
    fineiter=200,
    cool_fact=0.95,
    weight_node_dist=1.0,
    weight_border=1.0,
    weight_edge_lengths=1.0,
    weight_edge_crossings=1.0,
    weight_node_edge_dist=1.0
)

# List the layout coordinates for each vertex
for i, pos in enumerate(dh_layout):
    print(f'Vertex {i}: Position {pos}')
<|EOT|>
