The neighbour is he who dwells near your home and he has a great right on you. If he is a close relative (a member of your family) and that he is a Muslim, he has three rights on you: the right of the neighbourhood, the right of family ties and the right of Islam.
Types of Neighbor Hood and Rights
If he is a Muslim but he is not a close relative, he has two rights on you: the right of the neighbourhood and the right of Islam.
Similarly, if he is a close relative but he is not Muslim, he has two rights on you: the right of the neighbourhood and the right of family ties.
Finally, if he is not a close relative and he is not Muslim, there is the single right of the neighbourhood. Allah says,
{…(Show) kindness unto parents, and unto near kindred, and orphans, and the needy, and into the neighbor who is of kin (unto you) and the neighbor who is not of kin…} (Soorah an-Nisâ, 4 :36)
Hadiths on Rights of Neighbors
And the Prophet (ﷺ) said, ‘Jibril kept on enjoining the good treatment of neighbours to such an extent that I thought he would include neighbours as heirs’.
Among the rights of the neighbour on the neighbour is that he is beneficial to him, as much as he can, by his goods, his status and in being profitable to him.
The Messenger of Allah (ﷺ) said, ‘The best neighbour in the sight of Allah is the one who behaves best towards his neighbours.’ And he said, ‘That the one who believes in Allah and in the Last Day behaves best towards his neighbours’. He also said, ‘Whenever you prepare a broth, put plenty of water in it, and give some of it to your neighbours’.
To offer the neighbour gifts on occasions is part of the beneficence towards him, because this brings affection and make enmity disappear.
Rights of the Neighbour Upon his Neighbour
Among the rights of the neighbour upon his neighbour: that he does him no harm neither in words nor acts, as the Prophet (ﷺ) said, ‘By Allah! He is not a true believer! By Allah ! He is not a true believer! By Allah! He is not a true believer!’ The Companions said, ‘Who, O Messenger of Allah ?’ He said, ‘The one who does not preserve his neighbour from his own harm’. And in another version, ‘The one who does not preserve his neighbour from his own harm will not enter paradise’.
Nowadays, many people neglect the right of the neighbourhood and do not preserve their neighbours from their harm; you constantly see them argue and oppose between them, infringe their rights, harm them in words and in deeds. All this is contrary to the Command of Allah and His Prophet, it leads to the division between Muslims, repel the hearts and makes disappear the sanctity (of property, person and honour) from the other one.
Understand about the complete bibliography of Holy Prophet here.