Getting the minimum or maximum or using sorted depends on iterations over the object. In the case of dict, the iteration is only over the keys:

adict = {'a': 3, 'b': 5, 'c': 1}
min(adict)
# Output: 'a'
max(adict)
# Output: 'c'
sorted(adict)
# Output: ['a', 'b', 'c']

To keep the dictionary structure, you have to iterate over the .items():

min(adict.items())
# Output: ('a', 3)
max(adict.items())
# Output: ('c', 1)
sorted(adict.items())
# Output: [('a', 3), ('b', 5), ('c', 1)]

For sorted, you could create an OrderedDict to keep the sorting while having a dict-like structure:

from collections import OrderedDict
OrderedDict(sorted(adict.items()))
# Output: OrderedDict([('a', 3), ('b', 5), ('c', 1)])
res = OrderedDict(sorted(adict.items()))
res['a']
# Output: 3

By value

Again this is possible using the key argument:

min(adict.items(), key=lambda x: x[1])
# Output: ('c', 1)
max(adict.items(), key=operator.itemgetter(1))
# Output: ('b', 5)
sorted(adict.items(), key=operator.itemgetter(1), reverse=True)
# Output: [('b', 5), ('a', 3), ('c', 1)]