Friendship in the classroom
A recent law (not yet in effect) has been debated in Missouri about whether or not teachers could ‘friend’ students under 18 in social networking sites, such as facebook. There are certainly reasons for having such a law, in that teachers befriending students in an unofficial setting could result in security or privacy concerns; however, there are also benefits for such online network links to occur, such as providing extra help for classes or extracurricular activities. Also, a primary reason for repealing a law like this is that it could be deemed unconstitutional, violating free speech. It seems like such ‘friendships’ should be monitored, though not necessarily outright banned.
This got me thinking, what would happen if there was a graph in which the nodes had attributes, and nodes with certain attributes would be unable to have a link directly to a node with another particular attribute. It became an interesting thought experiment to consider connected components under these circumstances. Would it result in a graph with those groups in separate connected components, or would they still be in one giant component? Let’s say students are in group A, and they form a giant connected component, and teachers are in group B forming another connected component, and no edges could exist from A to B (this is an undirected graph). What would happen?
Obviously, if there were no other nodes in this graph, these would remain as two separate connected components, but in real life, this is certainly not the case. There is a whole group of people, say C, which are neither students nor teachers and may or may not be a friend of either, or both. These people would naturally form another giant connected component. The odds of at least one person from group C friending a student, and another friending a teacher are quite high. In fact, there would most likely be plenty of examples of people in C friending someone from both groups, such as a parent with and edge to their child and to a teacher of their child. So, unless the rules of the graph prevent even indirect paths between components, in a large enough network there will still only be one giant component.
http://yro.slashdot.org/story/11/09/08/1227229/Missouri-Hedges-On-Teachers-Cant-Friend-Students-Law
We are glad the ban has been repealed, however the overwhelming support for monitoring has been echoed by parents and schools alike.