<｜begin▁of▁sentence｜>### Instruction:
As a project coordinator, you have been tasked with organizing and coordinating a network analysis project for a team. The team has created a graph with vertices representing different aspects of the project and edges connecting them. You are now required to create a plot of the graph using a custom color palette for the vertices, using the AbstractVertexDrawer class in igraph. Your goal is to ensure that the visualization accurately represents the interconnections within the project and showcases the various vertices in a visually appealing manner.
### Response:
import igraph as ig
from igraph.drawing import plot
from igraph.drawing.colors import PrecalculatedPalette

# Define the vertices and edges
vertices = ['A', 'B', 'C', 'D']
edges = [(0, 1), (0, 2), (0, 3), (1, 3)]

# Create the graph
g = ig.Graph(edges=edges)
g.vs['name'] = vertices

# Define a layout for the graph
g_layout = g.layout('kk')

# Define a palette for coloring vertices
palette = PrecalculatedPalette(['red', 'green', 'blue', 'yellow'])

# Use the default plot function, which uses AbstractVertexDrawer internally
plot(g, layout=g_layout, vertex_color=[palette.get(0), palette.get(1), palette.get(2), palette.get(3)], target='graph.png')
<|EOT|>
