A graha is not read in isolation but through the several tables that make up a Panchanga and a chart. It rules no weekday, because the seven-day week is built from the seven visible grahas and the two nodes stand outside that set. It holds 7 years of the Vimshottari dasha cycle, and it is lord of three of the twenty-seven nakshatras, Ashwini, Magha and Mula, spaced nine apart so that the nine grahas cover the twenty-seven exactly three times over.
The Vimshottari dasha system divides a notional lifetime of 120 years among the nine grahas in a fixed order, Ketu, Venus, Sun, Moon, Mars, Rahu, Jupiter, Saturn and Mercury, with fixed lengths that sum to exactly 120. Which period a person begins life in is determined by the nakshatra the Moon occupied at birth, and how far through that period, by how far through the nakshatra the Moon had travelled.
In the scheme of dignities it is assigned an exaltation on which the classical sources do not agree, and dignity is what the classical rules for strength are built on, since a graha in its own sign or its exaltation is read as able to act and one in its fall as constrained.
Ketu is the descending node, the opposite point to Rahu and therefore always exactly a hundred and eighty degrees from it in any chart. The two are computed rather than observed, they always move retrograde through the signs, and neither has a weekday, since the seven-day week is built on the seven visible grahas and the nodes are additions to that older set.