Table 3 Preference rule table: rule for the new node addition in the subgraph based on the threshold \(\nu\) value and preference value
From: Theory of preference modelling for communities in scale-free networks
Preference value \({\bf{P_{\nu }^{(\alpha )}{(x,y)}}}\) | Fitness function rule | Decision of a new node addition |
|---|---|---|
\(0< P_{\nu }^{(\alpha )}{(x,y)} < 0.5 \quad P_{\nu }^{(\alpha )}{(x,y)} > \delta\) | \(f_{\mathcal {G}} > f_{\mathcal {G'}}\) | Not desirable for a community membership but it can have a very weak overlapping membership |
\(\qquad P_{\nu }^{(\alpha )}{(x,y)} = 0.5 \quad P_{\nu }^{(\alpha )}{(x,y)} > \delta\) | \(f_{\mathcal {G}} = f_{\mathcal {G'}}\) | Desirable for Community membership and it can have a weak overlapping membership |
\(1>P_{\nu }^{(\alpha )}{(x,y)}> 0.5 \quad P_{\nu }^{(\alpha )}{(x,y)} > \delta\) | \(f_{\mathcal {G}} < f_{\mathcal {G'}}\) | Strong community membership and it can have a strong overlapping membership |