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In the specific application to the TDS-1 the SH maximum degree was set to 20, this means no lithospheric field coefficients were determined and the reference lithospheric field model is the AUX-LIT field model (Olsen et al., 2013), used in DCO usually truncated to max SH degree 60.
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The maximum degree is dmax.
Stage 1: Isolated nodes in are analyzedStage 2: Nodes of maximum degree are included in.
So we must look at classes for which the maximum degree is not bounded.
The node with the maximum degree is considered as the attacked node, and with the changes of the parameter α, cascading failures will be investigated in this paper.
The maximum degree is not so important since, as it has been shown, in numerous areas, there is insufficient data to build an accurate model up to this wavelength.
The node with the maximum degree is assigned to the top layer, and the nodes connected to the node are put in the next layer.
From Table 4 we found that the γ values for the size and maximum degree are about 2.5 times bigger for STNs.
The maximum degree is the case that the cumulative probability equals 1/ N ; thus P(≥ K m ) = 1/ N, and from Equation (3), K m can be expressed as (12) K m = N p /2[ A (p + 1)] - A (p ).
It is difficult to reach a definite conclusion of the distribution's functional form with a very small range of degree values, but the maximum degree is less than 40 and the argument of crowding effect seems to hold here as well (Additional file 3, Figure S3).
The model so defined was chosen with basis functions defined over a cap with a semi-angle of 16°, in order to represent the main field and its secular variation, including the most significant harmonics of the regional geomagnetic field (the minimum and maximum degrees are approximately equal to 6.1 and 13.2, respectively).
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