The representation of the author collaboration network, considering only scientific publications available on Web of Science from the 1999–2026 period.
Network characteristics
Interpretation:
the co-authorship network compreses 6651 authors who published between 1999 and 2026, forming a total of 22722 connections (edges)
network density is very low at approximately 0.1%. This metric gives the proportion of actual connections relative to the total possible links (number of authors x (number of authors - 1) / 2 = 22.115 potential ties). The majority of the authors interact extensively within small, isolated scientific communities.
transitivity or global clustering coefficient is 0.81, representing the probability that two neighbors of a given node are also connected to each other. Consequently, in 81% of cases, authors B and C collaborate with each other if author A collaborates with both B and C. This high value indicates that within research teams, all members collaborate with one another, making thee teams highly cohesive. While scientific communities are very compact and research teams are small and well-defined, there are enough bridge authors connecting different research groups to maintain a short global distance.
network diameter (is 16) being defined as the longest shortest path between any two connected nodes in the network. The calculation method computes the minimum distance between every pair of nodes and selects the maximum value among them. In this network, any two connected authors are linked by at most 16 steps (meaning that if two authors have not collaborated directly, they are liked to a chain of intermediates co-authors), reflecting an intermediate speed of information dissemination. This long chain of collaboration between random authors emphases a well connected global structure despite the fragmentation.
network centrality or degree centralization shows the extent to which the network is dominated by a single node or a few key nodes. The obtain value is very low at 0.0096, reflecting the fact that the network is not centralized around a single author, and connections are uniform distributed among researchers.
average path length between any two authors is 6.87, which is a very low value. This implies that two authors are, on average, separated by fewer than 7 co-authors. While a part of the authors are directly connected, the remained are linked through one or more intermediaries authors (the network diameter is 16). It can be observed that the co-authorship network is highly interconnected at a global level.
Conclusions
The analysis of the author collaboration network within the QML&QC fields reveals a highly fragmented yet cohesive research network. The obtained values of density and centralization shows that the analyzed domain is not dominated by a single group/author. At the microscopic level the scientific communities are highly compact and well defined. At the macroscopic level, the average distance between authors remain low. The small value of average path length suggests a small world network phenomenon, driven by key bridge authors who successfully connect other isolated academic clusters. Consequently, while the network is decentralized, it maintains an efficient structural capacity for knowledge diffusion and collaborative scientific advancement.
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