When　the　edge　between　two　nodes　is　not　measured,　is　there　any　hint　to　know　the　edge　property,　and　will　the　inferred　edge　property　be　useful?　To　answer　these　questions,　this　paper　uniformly　defines　the　properties　of　unmeasurable　edges　in　generic　graphs.　For　an　unmeasurable　edge　　$(i,j)$　,　it　is　called　rangeable　if　its　length　is　unique　in　any　realization　of　the　graph,　rigid　if　the　number　of　its　possible　lengths　is　finite,　and　flexible　if　it　has　infinite　possible　lengths.　The　rangeable　edge　can　provide　deterministic　hidden　knowledge　as　if　the　edge　is　measured.　A　condition　for　an　unmeasured　edge　being　rangeable　in　2D　space　is　firstly　proposed,　based　on　which　a　centralized　identification　algorithm　(DRE)　is　designed.　However,　the　centralized　rangeable　edge　identification　has　the　overhead　of　global　information　collection.　Therefore　distributed　condition　and　algorithm　to　identify　rangeable　edges　are　further　investigated.　We　prove　that　an　unmeasurable　edge　　$(i,j)$　　is　rangeable　if　there　are　at　least　two　Disjoint　Minimally　Rigid　Branches　(DMRBs)　between　　$i$　　and　　$j$　.　The　unmeasurable　edge　　$(i,j)$　　is　rigid　and　flexible　when　the　number　of　DMRB　is　one　and　zero,　respectively.　A　distributed　Branching　and　Blacklisting　(BB)　algorithm　is　proposed　to　find　DMRBs,　so　that　rangeable　edges　are　identified　distributively.　Then,　the　applications　of　rangeable,　rigid,　and　flexible　edges　are　discussed.　Experimental　evaluations　show　that　the　centralized　and　distributed　algorithms　can　identify　a　rich　set　of　unmeasurable　but　rangeable　edges　in　distance　graphs,　even　more　than　the　number　of　directly　measured　edges.　Moreover,　BB　has　a　similar　identification　performance　as　the　centralized　DRE　algorithm　and　outperforms　existing　distributed　unmeasurable　edge　inference　algorithms　significantly.　IEEE