Show mercy to those on earth and the One above the heavens will show mercy to you

It is narrated from Sayyiduna Abdullah bin Amr (may Allah be pleased with them both) that he narrated it as a saying of the Prophet (peace and blessings be upon him), that he (peace and blessings be upon him) said: "Those who show mercy, al-Rahman shows mercy to them. Show mercy to those on the earth, and the One in the heaven will show mercy to you. The tie of kinship (al-rahim) is a branch from al-Rahman; so whoever joins it, Allah will join him, and whoever severs it, Allah will cut him off."
Imam al-Hakim says: All of these chains are sahih (authentic). I have examined their chains exhaustively, mentioning the Companions, so that no one imagines that the two Shaykhs did not leave out any authentic hadith.

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) that he said: I came to the Prophet (peace and blessings be upon him) while he (peace and blessings be upon him) was sitting in a red leather tent with about forty men. He (peace and blessings be upon him) said: "(The doors of conquest) will be opened for you; you will be helped and you will gain spoils. So whoever of you reaches that time, let him fear Allah, enjoin what is good, forbid what is evil, and maintain ties of kinship. And the example of one who helps his people in a wrongful matter is like a camel that is falling (into a well) and he is pulling it by its tail (meaning that he cannot save it from destruction)."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

Al-Qasim bin Mukhawwal al-Bahzi narrates from his father that he said: O Messenger of Allah! Give me some advice. He (peace and blessings be upon him) said: "Establish the prayer, pay the zakah, fast in Ramadan, perform Hajj of the House and Umrah, be kind to your parents, maintain ties of kinship, honour the guest, enjoin what is good, forbid what is evil, and stay with the truth wherever it is."
This hadith has a sahih (authentic) chain of narration through the Shaykhs of Yemen, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Salam (may Allah be pleased with him) that he said: When the Messenger of Allah (peace and blessings be upon him) arrived (in Madinah), the people rushed towards him, and it was said: The Messenger of Allah (peace and blessings be upon him) has arrived. I too went with the people to see him (peace and blessings be upon him). When I looked carefully at the blessed face of the Messenger of Allah (peace and blessings be upon him), I recognised that this face could not be the face of a liar. The very first thing he (peace and blessings be upon him) said was: "O people! Spread the greeting of peace, feed others, maintain ties of kinship, and pray at night while people are asleep; you will enter Paradise in peace."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that he said: O Messenger of Allah! When I see you, my heart is gladdened and my eyes are cooled; so tell me about everything. He (peace and blessings be upon him) said: "Everything was created from water." He said: I said: Tell me of a deed by which, if I do it, I will enter Paradise. He (peace and blessings be upon him) said: "Spread the greeting of peace, feed others, maintain ties of kinship, and stand (in worship) at night while people are asleep; then enter Paradise in peace."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that the Prophet (peace and blessings be upon him) said: "It is written in the Torah: Whoever would like his life to be long and his provision to be increased, let him maintain ties of kinship."
This hadith, with this wording, has a sahih (authentic) chain of narration, but the two Shaykhs did not record it; they only agreed upon the hadith of Yunus bin Yazid from al-Zuhri from Sayyiduna Anas.