On the existence and uniqueness of pairwise stable networks

Strategic Formation of Homogeneous Bargaining Networks

“…For instance, according to Hellmann (2013) (2013) and Hellmann and Landwehr (2014) are not applicable here, which gives rise to the upcoming more profound analysis.…”

“…Among other lines of research, some effort has been dedicated to gaining rather general insights regarding the existence, uniqueness and structure of stable networks. Therefore, we take results such as the ones found by Hellmann (2013) and Hellmann and Landwehr (2014) into account when considering stability issues in our model. We will show that crucial conditions are not met in our model, which implies that their results are not applicable here.…”

Evolution of social networks

“…There are several prominent centrality measures, mainly introduced in the sociology literature. 15 Among those is closeness centrality which is a rather intuitive definition of centrality considering the distances from a given node in 13 The definition is taken from Hellmann (2012). Other notions are introduced in Bloch and Jackson (2007) and Calvó-Armengol and Ilkiliç (2009).…”

“…Other notions are introduced in Bloch and Jackson (2007) and Calvó-Armengol and Ilkiliç (2009). However, it is shown in Hellmann (2012) that all definitions are equivalent.…”

“…[Hellmann (2012)] An iterated elimination of dominated links addition path is an improving path (G + 1 ...G + K ) with G + 1 = G ∅ (starting from the empty network) such that for all k = 1, ..., K − 1 :…”