Men and women in Egypt relate differently to each other than in the west, and perhaps differently to what you may be used to at home.
Personal space between members of the same sex may be closer than you expect, but men and women tend to stay further apart. However, as a tourist, and perhaps as a westerner, you may find the rules are bent a little for you.
Don’t be surprised to see men walking hand-in-hand or arm-in-arm, or male friends exchanging a hug and cheek kiss as well as a handshake upon meeting. This is a mark of affectionate respect. Female friends may also walk hand-in-hand or arm-in-arm.
It is rare to see men and women (couples) making overt shows of affection (you may see some arm-in-arm or hand holding) in Egypt and it is frowned upon for tourists to do so as well. Kissing in public, or on your tour bus, is likely to be not well received.
The handshake in Egypt is quite different from the west where a firm and at times prolonged shake is prized. Shaking hands in Egypt begins with a gentle open-handed “slap” (which become more vigorous, with a bigger back swing the more you know and like someone) followed by a soft and quick clasp.
While men and women do shake hands, if you are male it is probably best to wait until a woman extends her hand to you before shaking, even if she has shaken hands with other women in the group.