Hegselmann-Krause (HK) models exhibit complex behaviors which are not easily tractable through mathematical analysis. In this paper, a characterization of the steadystate behaviors of homogeneous HK models and sensitivity to confidence thresholds is discussed by commenting on existing and new numerical results. The typical decreasing of number of clusters and convergence time by increasing the confidence thresholds are discussed and motivations for the behavior of some counterexamples are provided. A tighter upper bound for the dependence of the number of clusters with respect to the confidence thresholds is proposed. Differences and analogies between the opinions' evolution for symmetric and asymmetric HK models are commented.
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