Considering that the Prophet (s) appointed the Commander of the Faithful, Ali (a.s) in an absolute and general way, the Holy Prophet's authority in its entirety, irrespective of whether it is mystical, religious or political, is also proven for Ali (a.s.).
According to Shiites, there is no doubt that the Wilayah (guardianship/authority) of the Commander of the Faithful that was announced and stressed by the Holy Prophet (s) in the event of Ghadir and on many other occasions before and after Ghadir includes all the cases where the Messenger of Allah (s) maintained wilayah (authority). Considering that the Prophet (s) established and led a government, we entertain no doubt that political authority or discretion over political affairs was one of the main aspects of his authority.
If we are to deal with your question in a more elaborate and detailed manner, we must say that in view of what happened after the Messenger of Allah (s) with the caliphate being denied to its principal owner, it was not justifiable for the general public in the succeeding generations to see the reign of government given to someone else in spite of all the explicit and implicit evidence which proved the right of the Commander of the Faithful, Ali (a.s.) to the caliphate. For this reason, the authors who were inclined to the predominant intellectual cult tried, as far as they could, to avoid mentioning the merits and privileges of the Commander of the Faithful, Ali (a.s) in their works. At times, they have sufficed to mentioning the selected parts, and if there was a mutawatir (narrator by many reporters) tradition which they could not deny, they would embark on justifying and interpreting them in a way such that would fit their own theological dogmas. The Ghadir tradition is one of the traditions mentioned partially in the authentic Sunni books because it was not possible for them to sensor it completely. The explicit statements by the Holy Prophet (s) with reference to the wilayah of Imam Ali (a.s.) are some of the proofs that have been authenticated in most of these books. Obviously, studying a narration with such explicitness and clarity begs the question: Why was Imam Ali (a.s.) denied political leadership despite the Prophet's sayings? That is where the justification comes to the scene with the wilayah in hadith interpreted as mystical authority or just as mere friendship and love. Such justifications have also been used in regards to other similar traditions. For instance, they say that the Prophet (s) introduced Ali (a.s) like Harun (Aeron). That is to say, Ali (a.s) is the Prophet's vizier and there is a difference between vizier and successor! Therefore, Ali (a.s) is not the Prophet's successor, rather he was his vizier during his lifetime and his viziership came to an end with the demise of the Prophet (s)!
Now, regardless of what Shiites believe, we shall, with reliance on Sunni books, discuss the Ghadir issue. In the event of Ghadir Khum, the Prophet (s) first asked Muslims: "Who is more appropriate for authority (awla) over you than yourselves?"
They replied: "God and His Messenger."
Thereupon, the Prophet (s) declared that Ali (a.s) was like him in all terms. In other words, Ali had the same trait and authority that the Prophet (s) had. He addressed the Muslim gathering as such: "Of whomsoever I am a master, this Ali is his master." It is interesting to know that following this event, Umar, the second caliph, came forward and said to Ali (a.s.): "Congratulations! You have become our master and the master of every believing man and every believing woman."
Another incident that is also endorsed by Sunni scholars and has been related in their reliable books is the story related to the Battle of Tabook. "The Messenger of God took a journey to Tabook, and he appointed Ali to succeed him in Medina. Ali said to the Prophet: `Do you leave me with the children and the women (and deprive me of taking part in the Jihad)?' The Messenger replied: `Are you not satisfied to be to me like Aaron to Moses, except that there shall be no Prophet after me?'" In fact, if the Prophet intended mystical wilayah (authority) in Ghadir, he could not have meant anything but political wilayah.
These two stories beg two basic questions:
1. Did the Holy Prophet's question (who is more precious and appropriate for authority over you than yourselves) relate to mystical authority only? Did it not include political authority so that we may consider the authority that was mentioned thereafter as only mystical, not political?
2. If the answer to the first question is in the negative and wilayah in the Ghadir tradition includes both mystical and political authority, then that is the point we want to assert and we do not need to further prolong the discussion. But if they still insist that the declared wilayah in Ghadir is mystical only, then the second question arises as follows: We have a person after the Prophet (s) who is at a high mystical rank and is also the bravest man militarily. He was considered to be the commander of the Prophet's army and has been his successor during the Battle of Tabook in the last years of the Prophet's life. He had also at times been tackling and administering the affairs of people in Yemen. Such a person is worthy of taking the government and the authority after the Prophet. Additionally, no party believed that the Prophet had appointed any particular person as his successor or as caliph after him, otherwise vowing allegiance to Ali (a.s.) would have been opposed to the command of the Messenger of Allah (s). Moreover, we see that, as per the Sunni books, this perfect mystic who maintained mystical authority over Muslims opposed the person who had come to power after the demise of the Holy Prophet (s); he did not pledge allegiance to him for six months. Shouldn't we give importance to his mystical authority in this regard? Is it not violation of the Prophet's command to be inattentive to his sayings and views? If in such matters, we do not pay attention to the words of a mystic who has authority over us, then what would be the benefit of his mystical authority?!
Hence, we conclude that the declared authority in Ghadir – be it mystical or political – will not justify the acts of those who prevented Imam Ali (a.s) from reaching the caliphate notwithstanding the fact that we believe that he, like the Holy Prophet (s), enjoyed mystical authority as well as political eligibility. In fact, to bring up such a discussion in regard to the Prophet (s) was not meaningful, nor was it ever propounded by anyone. The big question that arises here is: Based on the Holy Prophet's explicit statements about Imam Ali (a.s.) having all his traits, is it not strange to surrender the caliphate to someone other than him?!
 - On Yawm al-Dar, the Day of Mubahalah, the Battle of Tabook, when some individuals objected to the way he led the contingent led to Yemen etc.
 - See: Ahmad bin Hanbal, Al-Musnad, vol.1, pg. 118 – 119, Dar Sadir, Beirut, Ibn Majah Qazvini, Al-Sunan, vol.1, pp.43-45, Dar al-Fikr, Beirut and Sahih Tirmidhi, 1403 A.H., vol.5, pg. 297, Dar al-Fikr, Beirut.
 - Ahmad bin Hanbal, Musnad, vol.4, pg. 281, Dar Sadir, Beirut.
 - Bukhari, Sahih, 1401, A.H., vol.5, pg. 129, Dar al-Fikr, Beirut.
 - See: Bukhari, Sahih, vol.5, pp.82 & 83.