Statistical Analysis of Weighted Networks

Table 1

A comparison between random network and scale-free network (NM: network model, WD: weight distribution, WCC: weighted clustering coefficient, 𝑅²: squared correlation coefficient, 𝐹∣sig: 𝐹-ratio and corresponding significance, 𝑏₀, 𝑏₁: Estimated parameters of the linear model (constant and coefficient of the predictor variable relative perturbation norm) with corresponding 𝑡∣sig (𝑝-value)).

NM	WD	WCC	𝑅^2	𝐹∣sig	𝑏0	𝑡∣sig	𝑏1	𝑡∣sig
RandomNetwork Erdos-Renyi model	Uniform (Figure 3(a))	Zhang	0.994	1290.026∣0.000	0.372	69.092∣0.000	−0.362	−35.917∣0.000
		Lopez-Fernandez	0.994	1364.860∣0.000	0.371	71.072∣0.000	−0.362	−36.944∣0.000
		Onnela	0.997	2975.038∣0.000	0.370	100.354∣0.000	−0.376	−54.544∣0.000
		Barrat	0.013	0.101∣0.758	0.362	657.630∣0.000	0.000	−0.318∣0.758
		Serrano	0.000	0.001∣0.972	0.362	301.844∣0.000	0.000	−0.036∣0.972
	Normal (Figure 3(b))	Zhang	0.999	13629.467∣0.000	0.364	219.958∣0.000	−0.362	−116.745∣0.000
		Lopez-Fernandez	0.999	13711.182∣0.000	0.364	220.768∣0.000	−0.362	−117.094∣0.000
		Onnela	1	35769.842∣0.000	0.363	352.133∣0.000	−0.366	−189.129∣0.000
		Barrat	0.001	0.011∣0.920	0.361	1763.897∣0.000	0.000	−0.104∣0.920
		Serrano	0.027	0.224∣0.649	0.362	888.635∣0.000	0.000	−0.473∣0.649
	Exponential (Figure 3(c))	Zhang	1	102303.279∣0.000	0.362	599.496∣0.000	−0.362	−319.849∣0.000
		Lopez-Fernandez	1	109645.313∣0.000	0.362	619.969∣0.000	−0.362	−331.127∣0.000
		Onnela	1	24935.117∣0.000	0.363	291.250∣0.000	−0.369	−157.909∣0.000
		Barrat	0.441	6.305∣0.036	0.361	903.747∣0.000	0.002	2.511∣0.036
		Serrano	0.592	11.622∣0.009	0.361	700.433∣0.000	0.003	3.409∣0.009
Scale free Network Barabasi Albert Extended model	Uniform (Figure 4(a))	Zhang	0.982	425.202∣0.000	0.679	40.511∣0.000	−0.647	−20.620∣0.000
		Lopez-Fernandez	0.982	427.643∣0.000	0.680	40.421∣0.000	−0.651	−20.680∣0.000
		Onnela	0.996	2269.81∣0.000	0.672	87.611∣0.000	−0.685	−47.643∣0.000
		Barrat	0.106	0.945∣0.360	0.655	356.437∣0.000	0.003	0.972∣0.360
		Serrano	0.096	0.854∣0.382	0.655	162.161∣0.000	0.007	0.924∣0.382
	Normal (Figure 4(b))	Zhang	0.998	3375.047∣0.000	0.652	109.145∣0.000	−0.650	−58.095∣0.000
		Lopez-Fernandez	0.998	3510.742∣0.000	0.652	111.183∣0.000	−0.651	−59.252∣0.000
		Onnela	1	25056.870∣0.000	0.656	296.796∣0.000	−0.655	−158.294∣0.000
		Barrat	0.016	0.129∣0.729	0.655	368.559∣0.000	0.001	0.359∣0.729
		Serrano	0.018	0.150∣0.709	0.655	170.560∣0.000	0.003	0.387∣0.709
	Exponential (Figure 4(c))	Zhang	0.999	13635.348∣0.000	0.656	215.181∣0.000	−0.667	−116.770∣0.000
		Lopez-Fernandez	0.999	13883.081∣0.000	0.656	216.885∣0.000	−0.668	−117.826∣0.000
		Onnela	1	21450.540∣0.000	0.658	269.459∣0.000	−0.670	−146.460∣0.000
		Barrat	0.119	1.077∣0.330	0.656	745.786∣0.000	0.002	1.038∣0.330
		Serrano	0.088	0.771∣0.405	0.655	388.730∣0.000	0.003	0.878∣0.405