1999
DOI: 10.1016/s0165-4896(98)00013-4
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Values of games with probabilistic graphs

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Cited by 47 publications
(51 citation statements)
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“…Now, we are ready to define the Weighted Attachment Centrality for node-and edge-weighted graphs. For a graph G = (V, E, 1, ρ) with unweighted nodes, the Weighted Attachment Centrality is equal to the Probabilistic Myerson value, defined by Calvo et al [1999] with characteristic function f * G . Based on Theorem 8, we get the following two axiomatizations of the Weighted Degree Centrality and the Weighted Attachment Centrality.…”
Section: Node-weighted Graphsmentioning
confidence: 99%
“…Now, we are ready to define the Weighted Attachment Centrality for node-and edge-weighted graphs. For a graph G = (V, E, 1, ρ) with unweighted nodes, the Weighted Attachment Centrality is equal to the Probabilistic Myerson value, defined by Calvo et al [1999] with characteristic function f * G . Based on Theorem 8, we get the following two axiomatizations of the Weighted Degree Centrality and the Weighted Attachment Centrality.…”
Section: Node-weighted Graphsmentioning
confidence: 99%
“…In this last case, w l ∈ [0, ∞), for all l ∈ γ. Calvo et al (1999) propose to interpret each weight as the probability of the corresponding relation and to assume the links independence.…”
Section: Weighted Graphsmentioning
confidence: 99%
“…Remark 3.4 If (N, γ w ) is a weighted network in which, for each l ∈ γ, w l is interpreted as the probability of a direct relation between its two incident nodes, and these probabilities are considered as independent (as in Calvo et al, 1999) then, for R connected in γ and T ⊆ R:…”
Section: Weighted-graph Restricted Gamesmentioning
confidence: 99%
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“…In other words, these coalitions are those corresponding to the communication situations between the players: A ⊆ N is feasible if and only if there is a communication chain for any pair of players of A. More details about games with communication graphs may be found in Calvo, Lasage, and Nouweland (1999) and van den Brink, van der Laan, and Pruzhansky (2004).…”
Section: Regular Gamesmentioning
confidence: 99%