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Table 1 Main indices of clique network used in this paper

From: Shannon entropy in time-varying semantic networks of titles of scientific paper

Index Description
nq Number of titles in the initial configuration.
n Number of network vertices in the final configuration.
m Number of edges in the final configuration.
m0 Number of edges in the initial configuration.
n0 Number of vertices in the initial configuration, n0n.
#(vi) Frequency of vertex i in the initial configuration, i.e., the number of titles that contain vertex i (1≤#(vi)≤nq).
#(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)≤nq, and i,j=1,2,...,n, with ij and (i,j)=(j,i).
qi Title size i. Number of vertices of title i in the initial configuration, (1≤inq).
qmin. Number of vertices of the smallest title in the initial configuration, (1≤qminn).
qmax. Number of vertices of the largest clique in the initial configuration, (1≤qmaxn).
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 ki 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.
  1. “Initial configuration” is related to the isolated cliques, and “final configuration” is related to the built “network of cliques”. The indices are valid for each time window considered