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As expected, this plot clearly suggests that ER random networks are inherently degree weighted, i.e., P k1, k2) ∝ k1 k1.
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TA-WeightedDegree uses the degrees weighted by the probability from topic mixtures, and selects top k nodes with the highest weighted degrees.
One utility of knowing that a network is degree-weighted is to use the probabilistic interpretation to find nodes that deviate from degree-weighted probability.
Of the networks analyzed here, only that of P. falciparum shows a degree-weighted tendency throughout.
For Plasmodium falciparum, degree-weighted behaviour is exemplary throughout, thus no such value could be determined.
The results further suggest that degree-weighted behaviour may be an indication, or property, of randomness.
To illustrate the concept of inherent randomness in networks displaying degree-weighted behaviour, we show how Erdös-Rényi (ER) random graphs [ 10, 11] also exhibit a degree-weighted characteristic.
Nonetheless, examination of the connectivity profile in ER networks will shed light on the interpretation of degree-weighted behaviour.
It is thus of importance to both qualitatively and quantitatively ascertain the extent of degree-weighted behaviour in biological networks.
Further insight into the degree-weighted nature of PPI networks may be obtained from analyses of the interacting protein pairs at more elementary levels.
Degree-weighted behaviour was then established by comparing the probabilities P k1, k2) of interaction with the products k1 k2 of the degrees.
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