Many times there is a need to define your distance function. I found this answer in StackOverflow very helpful and for that reason, I posted here as a tip.

All of the SciPy hierarchical clustering routines will accept a custom distance function that accepts two 1D vectors specifying a pair of points and returns a scalar. For example, using fclusterdata:

import numpy as np
from scipy.cluster.hierarchy import fclusterdata

# a custom function that just computes Euclidean distance
def mydist(p1, p2):
    diff = p1 - p2
    return np.vdot(diff, diff) ** 0.5

X = np.random.randn(100, 2)

fclust1 = fclusterdata(X, 1.0, metric=mydist)
fclust2 = fclusterdata(X, 1.0, metric='euclidean')

print(np.allclose(fclust1, fclust2))
# True
 

Valid inputs for the metric= kwarg are the same as for scipy.spatial.distance.pdist. Also here you can find some other info