Is modularity of -1 possible

Question

Wikipedia mentions that modularity of a network is within the range [-1,1).But if we consider a complete graph with n nodes and assign different community to each node than the modularity turns out to be -1/n. I can't quite figure out how to reduce modularity further. Can you give an example of network with -1 modularity.

Answer 1

Using your definition of the modularity of -1/n, an example of a network with -1 modularity is simply a network with only one node. When $n = 1$, $-1/n = -1/1 = -1$