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def interval_graph_coloring(graph):

'''The input graph is represented as an adjacency matrix since all we need is edge information about the graph'''

m = graph.shape[0]

color = [1] * m

number = 1

for i in range(0, m):

for j in range(0, m):

if graph[i, j] == 1 and color[i] == color[j]:

color[j] = color[i] + 1

if color[j] > number:

number = color[j]

return color,number