I introduced graph theory to my son when he was about 8 or 9 years old. By Nature, he's a networker (like to connect to people) so "friends of a friend" was very intuitive to him.
I have also tried to introduce the concepts to teenagers. In Denmark, we have an annual, national science weeks in primary and secondary schools. I have given http://www.slideshare.net/geisshirt/naturvidenskabsfestival-... as a talk/lecture at 4-5 schools and most 13-15 years old children get the ideas quickly - Facebook and other social medias are a big help :-)
I have also tried to introduce the concepts to teenagers. In Denmark, we have an annual, national science weeks in primary and secondary schools. I have given http://www.slideshare.net/geisshirt/naturvidenskabsfestival-... as a talk/lecture at 4-5 schools and most 13-15 years old children get the ideas quickly - Facebook and other social medias are a big help :-)