On the definition of fractional clique number

Question

The fractional clique number of a given graph is defined in mathworld as the maximum possible sum of values of any of its fractional cliques. But, why such sums are upper-bounded?

Answer 1

The maximum sum of values on an independent set is $1$. In particular, the value on a single vertex is bounded above by $1$. For a finite graph with $n$ vertices, the sum of values is then bounded above by $n$. This is achieved on the complete graph.