For better or worse, 'connectome' is a legit term used in the field. It's relatively newish (quickly skimming the literature, first mention was in a 2005 article). It follows the naming convention setup by 'genome', and includes many variants:

- genome (set of dna material in a cell)

- exome (set of exonic dna material)

- transcriptome (set of all messenger RNA)

- proteome (set of proteins in a cell)

- interactome (set of all interactions in a cell -- protein, small molecular, etc)

- metabolome (set of all small molecular compounds / interactions in a sample)

- connectome (set of all connections in the brain -- e.g. a wiring diagram)

etc etc