The Top Candidate (TC) method is an iterative voting-based algorithm originally designed to detect experts in a community and later applied to identify innovators and early adopters in social networks [2, 3]. The TC method focuses on identifying a stable set of mutually reinforcing expert candidates whose nominations support one another. The approach relies on the assumption that experts tend to nominate other experts more reliably than non-experts. The algorithm proceeds through the following steps:

  1. Initialization: all nodes are initially considered experts.
  2. Nomination: each node selects an \( α \)-fraction of its most popular neighbors as nominees, with popularity defined as the (weighted) in-degree and \( α \in [0, 1] \).
  3. Elimination: nodes that receive no nominations are removed from the expert set. All nominations issued by these removed nodes are discarded as well.
  4. Update: the elimination in Step 3 may cause additional nodes to lose all incoming nominations. These nodes are likewise removed, and the process is repeated until no further removals occur.
The resulting set of nodes constitutes the stable expert set . A set \( S \subseteq \mathcal{N} \) is stable if (i) every node in \( S \) is nominated by at least one other node in \( S \) and (ii) all nominees of any node in \( S \) are also contained in \( S \). The parameter \( α \) controls the exclusiveness of the selection: smaller values of \( α \) lead to more restrictive nomination sets and thus smaller expert groups, whereas larger values of \( α \) generally produce more inclusive and larger stable sets.

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Sziklai, B. (2018). How to identify experts in a community?. International Journal of Game Theory, 47(1), 155-173. doi: 10.1007/s00182-017-0582-x.
[3] Sziklai, B. R., & Lengyel, B. (2022). Finding early adopters of innovation in social networks. Social Network Analysis and Mining, 13(1), 4. doi: 10.1007/s13278-022-01012-5.