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At this stage we calculate various measures, such as Mutual Information and entropy (described below and in supplementary material [see Additional file 4]), which characterize the strength of node relationships and overall uncertainty.
Figure 8 Strength of node connectivity visually mapped from values of s i along (A -(B) Ivory Coast Tribal ; (C - D) Ivory C - D AdmIvory Coast ; Administrativertuguese andinistrativE -oundaries.
The intra-layer strength of a node-layer (i alpha )) is (k_{i alpha )}), and (c_{i alpha )}) is the inter-layer strength of node i with respect to its connections to its counterparts in different layers.
For node i, we sum over j the product of the activity level of node j times the interaction strength of node j on node i.
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They are defined as k_{i alpha )} = sum_{j in {mathcal{{N}}} (i) } w_{ij}^{alpha } quad text{and} quad c_{i alpha )} = sum_{beta } d_{(i)}^{alpha beta }, so that the total strength of node-layer (i alpha )) is the sum, i.e., (kappa_{i alpha )} = k_{i alpha )} + c_{i alpha )}).
The strength of nodes and their strength distribution, weighted clustering coefficient, and average shortest paths of the price network in different periods were calculated.
The n-to-1 connectivity <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0008525.e190.PNG" class= inline-graphic"/> (strength of nodes) characterized how the strength of the relationship decreases with the distance between the two regions [44], [45].
A bootstrap of 1,000 replications was used to estimate the strength of nodes in the tree [ 40].
We also made a control analysis to investigate whether the total connection strength of a node depended on the node's firing rate to the most preferred stimulus direction, and the analysis revealed no significant correlation (r = 0.23; P > 0.05).
Indeed, the normalized weight (x_{ij}) depends on the strength (s_{i}) of node i and therefore will be generally different from (x_{ji}).
The strength si of node i is defined as the sum of the weights wi,j of all links between node i and its neighbors Ni, <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0011569.e002.PNG" class= inline-graphic"/>.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com