Evolution of the Physics Citation Network with Motifs

Citation networks contribute to the analysis and research of scientific activities. We studied the evolution of the physics journal Physical Review Letters(PRL) citation network from 1958 to 2015 through the perspective of network science. The results show that the scale of the PRL citation network is expanding faster and faster in general, however, the growth rate slows down in recent years. No matter how the network evolves, its in-degree distribution always follows the power-law distribution. Whereas the out-degree distribution follows the exponential distribution obviously. As a directed and unweighted network, the four degree-degree correlation coefficients of the citation network are all positive. Furthermore, we analyze the citation network with three-node directed motifs to disclose deeper information with higher-order network structure. The citation network is mainly composed of motifs M
5
, M
8
, M
9
and M
10
, accounting for more than 98%. And the number of these four motifs has an extremely strongly positive correlation with the number of nodes and edges. M
10
has the highest proportion in the citation network and its proportion increases every year. The year difference distributions formed by nodes at similar positions but in different motifs are quite similar, yet more heterogeneous in M
5
.