Lebanon: Would you consider North Africans (Algerians, Moroccans, Tunisians etc) as Arabs?

I'm half Lebanese half Palestinian and I went to Algeria over the summer cos my uncle lives there. When I went there I saw Algerians who looked arab, white, black, brown, mixed race so in appearance I would say the people generally looked like a mix of Arab, Southern European, and Black. Being of Lebanese and Palestinian descent I can speak both Levantine Arabic and standard fus'ha Arabic. When I was talking to the Algerians I found it hard to understand their Arabic dialect so they spoke to me in fus'ha. Since all these things are the case in Algeria, I think I would encounter the same things in other North African countries like Morocco and Tunisia because there basically the same people. Since North Africans are generally mixed and there Arabic dialect is hard to understand for the typical Arab middle easterner (Lebanese, Palestinian, Syrian etc) would you consider North Africans arabs?