I don't believe there are any pre-defined or standardised cut-offs due to the fact that network metrics can vary tremendously based on numerous other parameters, such as:
- distance metric used for network construction (e.g. Euclidean distance, correlation, etc)
- total number of nodes / vertices
- any pre-filtering on edge values (e.g. removing weak edges)
- the nature of the data, e.g., a network constructed from
differentially expressed genes using 1 group of samples in which they were found to be differentially expressed will likely produce a 'stronger' network than one produced from randomly selected genes
- whether you're plotting just a graph or a minimum spanning tree of
- et cetera
Also, these scores are presented differently in different studies. For example hub scores, closeness centrality, and betweenness centrality can either be presented as scaled to 0-1 or as 'raw' scores. Degree is obviously just degree..
Thus, your choice of threshold should be based on the rank of the scores. Higher scores obviously indicate a more important vertex. Once you take a look over the results, you'll get a feeling of where you should be setting thresholds.
Just my take.