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Table 1 Statistics of single-layer networks and the aggregated (AGG.) network, including 1. the number of active nodes N[α], i.e., nodes that are connected by at least one in-/out-link (Nicosia and Latora 2015); 2. the total number of edges E[α]; 3. the average strength 〈s[α]〉; 4. density D[α] measuring the ratio of the number of edges to maximum possible number of edges; 5. fraction of nodes in the giant weakly connected component %G[α]; 6. reciprocity r[α] quantifying the likelihood of nodes with mutual links; 7. the Kendall’s τ correlation between in- and out-strengths \(\tau \left (s_{in}^{[\alpha ]}, s_{out}^{[\alpha ]}\right)\). 8. global clustering coefficient C[α] which measures the extent that two neighbors of a node are connected; 9. assortativity coefficient by strength \(A_{s}^{[\alpha ]}\), i.e., the correlation between the out-strengths of source nodes and the in-strengths of destination nodes (Newman 2003)

From: Characterizing dynamic communication in online eating disorder communities: a multiplex network approach

Network Mental Social Fitness Body Thinspo AGG. (all αs)
N [ α] 9381 28,959 17,689 11,199 14,156 55,164
E [ α] 17,306 54,609 34,040 17,881 27,807 140,330
s[α] 3.55 2.89 2.94 2.46 2.96 4.32
D [ α] 1.97 ×10−4 6.51 ×10−5 1.09 ×10−4 1.43 ×10−4 1.39 ×10−4 4.61 ×10−5
% G [ α] 76.55% 89.17% 83.84% 73.87% 88.87% 95.67%
r [ α] 0.24 0.19 0.36 0.45 0.33 0.29
\(\tau \left (s_{in}^{[\alpha ]}, s_{out}^{[\alpha ]}\right)\) -0.06 -0.04 0.09 0.21 0.13 0.11
C [ α] 0.06 0.04 0.03 0.03 0.01 0.03
z(C[α]) 40.70 198.96 61.25 109.21 6.29 160.67
\(A_{s}^{[\alpha ]}\) -0.08 -0.07 -0.1 -0.02 -0.08 -0.1
\(z\left (A_{s}^{[\alpha ]}\right)\) -10.64 -17.24 -19.05 -4.60 -14.04 -37.80
  1. Values of z(x) are z-scores for the empirical results based on null models. For each property x of a network, we generate 1000 randomized networks via the configuration model (Newman and Girvan 2004) and measure the property in these randomized networks. Then, the deviation of x from randomness is quantified by a z-score: z(x)=(x−〈x〉)/σx, where 〈x〉 is the mean value of the property in randomized networks and σx is the standard deviation