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We investigate the rainbow k -connectivity rc k and (t , k) -rainbow index rx t , k of the inhomogeneous random graph G (n , p) , where any two vertices i and j are joined by an edge e i j with probability p (e i j) independently of all other edges, and p = { p (e i j) }. We show that the known threshold functions for the monotone properties rc k (G (n , p)) ≤ r and rx t , k (G (n , p)) ≤ t for integers k , r and t in the Erdős–Rényi random graph G (n , p) can be extended to 'threshold landscapes' in terms of G (n , p). In contrast to the traditional plain thresholds characterized as a watershed, our threshold landscapes have two surfaces that are inherently interwoven with each other. This sheds some light on the network connectivity as appropriate trade-offs are allowed and is potentially applicable in network science where connections are not always equal. [ABSTRACT FROM AUTHOR]