Detecting a most closeness-central clique in complex networks

•The maximum-distance-closeness-central clique problem is introduced and studied.•The total-distance-closeness-central clique problem is also introduced and studied.•The decision version of these problems are proven to be NP-complete.•New integer programs and the first combinatorial exact algorithms are proposed.•Proposed methods offer at least 83-fold speed-up on majority of benchmark instances.