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Applied Network Science

Table 2 Calculation of diffusion probabilities for two scenarios

From: A novel regularized weighted estimation method for information diffusion prediction in social networks

\(Scenario 1,\)

\(isDiffused\left(\left(u, v\right),{ D}_{0}\right)=1\), \(isDiffused\left(\left(u, v\right),{ D}_{1}\right)=1\)

\(weight\left(\left(u, v\right),{ D}_{0}\right)=1, weight\left(\left(u, v\right),{ D}_{1}\right)=W\left(2\right)=\frac{1}{2}\)

\({P}_{uv}^{WEDP}=\frac{1\times 1+\frac{1}{2}\times 1}{1+\frac{1}{2}}=1\)

\(isDiffused\left(\left(j, v\right),{ D}_{0}\right)=0\), \(isDiffused\left(\left(j, v\right),{ D}_{1}\right)=1\)

\(weight\left(\left(j, v\right),{ D}_{0}\right)=1, weight\left(\left(j, v\right),{ D}_{1}\right)=W\left(2\right)=\frac{1}{2}\)

\({P}_{jv}^{WEDP}=\frac{1\times 0+\frac{1}{2}\times 1}{1+\frac{1}{2}}=1\)

\(Scenario 2,\)

\(isDiffused\left(\left(u, v\right),{ D}_{0}\right)=0\), \(isDiffused\left(\left(u, v\right),{ D}_{1}\right)=1\)

\(weight\left(\left(u, v\right),{ D}_{0}\right)=1, weight\left(\left(u, v\right),{ D}_{1}\right)=1\)

\({P}_{uv}^{WEDP}=\frac{1\times 0+1\times 1}{1+1}=\frac{1}{2}\)

\(isDiffused\left(\left(j, v\right),{ D}_{0}\right)=1\), \(isDiffused\left(\left(j, v\right),{ D}_{1}\right)=0\)

\(weight\left(\left(j, v\right),{ D}_{0}\right)=1, weight\left(\left(j, v\right),{ D}_{1}\right)=1\)

\({P}_{jv}^{WEDP}=\frac{1\times 1+1\times 0}{1+1}=\frac{1}{2}\)

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