Considering clustering measures: Third ties, means, and triplets

The Friendship Paradox for Weighted and Directed Networks

“…Generalization of clustering coefficients to graphs endowed with a weight function on edges has been considered by several authors (see for instance [18,31]). The process leading to the definition of γ v in (B.4) above extends naturally to such graphs, with similar connections to existing methods (see Theorem B.2, below).…”

“…note, for instance, the in-degree or out-degree of v in G, some other graph dependent measure such as betweenness or closeness (see for instance [31] and the references therein), or some attribute extraneous to G, itself, such as biomass in a food web.…”

“…For further recent work related to the friendship paradox, see for instance [12,20,24,31,15,33,22,18,32,36], and for further information on random walks on graphs, see for instance [26,1,25,7].…”

mCAF: a multi-dimensional clustering algorithm for friends of social network services

“…Several studies have explored weighted network analyses (Barrat et al 2004; Phan Binh and Fjeldstad Øystein 2013; Tore Opsahl 2009) and defined open triplets, which are composed of two edges, and closed triplets, which are composed of three edges. Additionally, a triangle is defined as containing three closed triplets.…”

“…One type of method (i.e., the SCAN method) uses the composition of the structure of an entire network (Xu et al 2007). The other type of method only considers the weights of the edges (Barrat et al 2004; Phan Binh and Fjeldstad Øystein 2013; Tore Opsahl 2009). We believe that both factors are important to cluster friends; thus, the proposed approach in this study combines these two concepts.…”