From: Shannon entropy in time-varying semantic networks of titles of scientific paper
Index | Description |
---|---|
n_{q} | Number of titles in the initial configuration. |
n | Number of network vertices in the final configuration. |
m | Number of edges in the final configuration. |
m_{0} | Number of edges in the initial configuration. |
n_{0} | Number of vertices in the initial configuration, n_{0}≥n. |
#(v_{i}) | Frequency of vertex i in the initial configuration, i.e., the number of titles that contain vertex i (1≤#(v_{i})≤n_{q}). |
#(i,j) | Frequency of edge (i,j) in the initial configuration, i.e., the number of titles that contain the words i and j, 1≤#(i,j)≤n_{q}, and i,j=1,2,...,n, with i≠j and (i,j)=(j,i). |
q_{i} | Title size i. Number of vertices of title i in the initial configuration, (1≤i≤n_{q}). |
q_{min}. | Number of vertices of the smallest title in the initial configuration, (1≤q_{min}≤n). |
q_{max}. | Number of vertices of the largest clique in the initial configuration, (1≤q_{max}≤n). |
〈k〉 | \(\langle k \rangle =\frac {\sum _{1}^{n}k_{i}}{n}=\frac {2m}{n}\), where 〈k〉 is the average degree of an undirected network and k_{i} is the degree of a vertex i, that is the number of edges incident on the vertex i. |
\(k_{i}^{hub}\) | \(k_{i}^{hub}\geq \langle k \rangle + 2\sigma \), are the degree values of the hubs, that is, vertices of very high degrees. σ is the standard deviation of the degree distribution. |