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Table 1 The notations and their meaning used in the preference relation approach

From: Theory of preference modelling for communities in scale-free networks

Meaning Abbreviation
Input graph on which communities are to be detected \(G=(V,E)\)
Out-degree: number of links outside graph G \(K_{out}^{\mathcal {G}}\)
In-degree: number of links inside graph G \(K_{in}^{\mathcal {G}}\)
Internal-links: for node i, links shared with neighboring nodes belonging to community c \(k_i^{int} (c)\)
External-links: for node i, links shared with neighboring nodes not belonging to community c \(k_i^{ext} (c)\)
Preference implication for comparing x and y \(P_{\nu }^{(\alpha )}{(x,y)}\)