Eccentricity of families not so much when head’s away (9)

'eccentricity' is the definition.
(kinky can mean abnormal or eccentric)

'families not so much when head's away' is the wordplay.
'families' becomes 'kin kin' ('kin' means one's family).
'not so much' becomes 'less' (I've seen this before).
'when head's away' means to remove the first letter.
'less' with its first letter removed is 'ess'.
'kinkin'+'ess'='KINKINESS'

'of' is the link.