Microstate connectivity alterations in patients with early Alzheimer’s disease

Table 1 Graph measures as calculated for each subject

Name		Formula	Reference
degree		= mean(W) (all links of a single node)
Average clustering coefficient	Cw	Cw = mean(C)	[38]
Average clustering coefficient	Cw	$ {C}_i = \frac{\underset{l\ne k}{{\displaystyle {\sum}_{k\ne i}}{\displaystyle {\sum}_{l\ne i}}{W}_{ik}{W}_{il}{W}_{kl}}}{\underset{i\ne k}{{\displaystyle {\sum}_{k\ne i}}{\displaystyle {\sum}_{l\ne i}}{W}_{ik}{W}_{il}}} $	[38]
Normalized clustering coefficient	Gamma	Cw / Cr	[49]
Normalized clustering coefficient	Gamma	(Cr = average of 50 randomized input matrices)	[49]
Average path length	Lw	$ L = \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$W$}\right. $	[38]
		L = ∞ (if W = 0)
		$ Lw = \frac{1}{\frac{1}{N\left(N-1\right)}*\ {\displaystyle {\sum}_{i=1}^N}{\displaystyle {\sum}_{j\ne i}^N}\left(1/{L}_{ij}\right)} $
Normalized average path length	Lambda	Lw / Lr	[49]
Normalized average path length	Lambda	(Lr = average of 50 randomized matrices)	[49]
Degree correlation	Rw	Rw = Pearson correlation of degrees of pairs of neighbors	[50]
Degree diversity	Kw	$ Kw=\frac{\left\langle degre{e}^2\right\rangle }{\left\langle degre e\right\rangle } $	[44]
Radius	Radius	Ec = maximal shortest path of single node	[51]
Radius	Radius	Radius = = min (Ec)	[51]
Diameter	Diameter	= max(Ec)

ISSN: 1758-9193