The are not linked.  In fact they should be mutually exclusive in a relationship.   They are the exact opposites.

You can not love and hate the same person.  If you do hate them you do not really love them.  And if you love them you do not really hate them.  If there are times that you hate them, and times that you love them (I think this is what you imply), you need to have a good look at the relationship you are dealing with, because in my opinion, it is not a healthy one.

Thanks for your replies guys!

@Sumit: I really like your mindset! You seem to always look at the bright side of life, and I have to admit that it's something I have to work on...
If I did understand you, you don't think such an antagonism can exist unless the people involved ignore what a relationship based on love is truly about. If so, I don't think we will ever seize this "pure form of love" as it has, to me, different shapes according the person you're referring to. But I agree with you when you say that we should be with someone that is willing to grow the bond we're supposed to have in a relationship. 
Thank you for your warm words! :) :)

Aaah @Sudeep :) :) Yes! You got a point! I think we all know around us people who used to be in love and are now their worst enemies...How sad! But your conclusion says it all: we're free to choose to keep on holding or to drop the hand that did us wrong. 
And I would add that this is when - whether you hold it or drop it - you know if the relationship in question is strong/healthy enough to survive the darkest episodes of its existence!
Thanks dear Sudeep for sharing your opinion! :)

@Karl: your answer is really interesting! What would your respond to someone who would claim that they were genuinely in love with the person they now hate? Do you think that feelings are immutable? (genuine curiosity here :))
I think you're right when you say that going through such downs in your emotions repetitively might be an indicator of an unhealthy relationship!
Thanks for you answer! 

@Guyomar: I studied latin, but had to look for the translation of this quote (that I did not know) ^^. I like your approach!
Yes, that's exactly that sometimes (with emotions in general): something that you feel but can't explain...Especially when you're torn between two opposite feelings.
Thank you very much for sharing! 

hehe.. ok so let me complete that part :)

actually a relationship stands on ruthne away... it is beauty of any relation... we loves someone, we tries to make her happy but still sometimes we have right to get offend, we can agree or disagree on some points, but still we spent life together and cares for each other that is chemistry :) actually we can't live life in same mode with only one immotion yaar just imagine we starts saying only yes to the beloved like god's words :p then where is the immotion (it is like a season change) every feeling is important. it is part of life actually... it is the beauty of strong relation that we knows merits and demerits of each other we understands each other and lives for life time with that person :)

and if you are saying about that few people who loves someone and after a season( i mean few months or year) they starts ignoring like (natural fractures), and suddenly feelings changes from love to hate... then that person does not know the exact pure form of love and relationship... they are like desert island between the rivers... no habitation even water is available :))...so, better is live with the person who understand that bond. my opinion for you is.. be what you are, remain positive, thank god, do good for everyone.. by those things you will found a new world here full of energy, piece and love :)

Best wishes and Regards :)

Actually you are asking about feelings... we are human beings a social animal.... we have feelings like love, hate, fear, anger, mercy, devotion etc. these are part of our life.... each feeling comes from inside by our observations. 

so now come to your point... yes they(love, mercy, devotion linked with soul and heart) whereas fear, hate and anger are primiary linked with brain. :) because our soul and heart never think wrong for anyone and inspires us to be noble person. but, brain is responsible for all kind of fear and hates because it observes and calculates this is good that is bad... :)

so, my suggestion is use your inner soul and heart as much as possible and u will find that the whole world is filled with love... you will see love- love everywhere... :) 

Bless you :)

Murielle, let me answer your question as per my understanding about these two birds Love and hate hahha:)

Yes, I agree that love and hate are intrinsically linked in most of the relations. But the question is Why? Maybe for our expectation! As long as our expectation is on the track, love is the captain of our relationship but if somewhere we get hurt by the same people we love the most then suddenly, hate comes into the play.

Be it a family relation or friendly relation or a love relation, in each and every type of relationship, we put our trust, hope, care and other things that turn it into a better relationship. At this point of time, we are in love with the people we have in our relationship, but if in case, someone we care or trust or love the most hurt us by breaking our trust or not caring our importance, we feel kind of uncomfortable and slowly, maybe after sometimes, it turns into a hateful relationship. There are so many examples you can find where two best friends or two best couples became the best/worst enemy of each other.

So, yes, love and heat go hand in hand but it's up to us whose hand we want to hold even if something goes wrong:)