Table 1 Definition of social network terms and their meaning in this study

Node

The node is the basic element of the network being connected. In this study, nodes represent organisations that were affiliated with authors who co-published with the UCRH

Edge or tie

An edge or tie connects two nodes in a network and indicates a relationship between the two. In this study, an edge between two organisations indicates co-authorship of at least one publication

Degree-related measures

Degree-related measures show the number of ties coming from each node and going to each node. A higher co-authorship activity is reflected in higher median and mean degree, and a more connected network overall. Organisations with the degree of zero collaborated exclusively with UCRH without the involvement of any other organisation. Nodes with the maximum degree have the highest number of mutual collaborators in common with UCRH

Degree variance

Degree variance measures the spread of co-authoring activity between high-degree and low-degree nodes. It is also a way to conceptualise centralisation, used especially when dealing with networks of significantly different sizes. High degree variance indicates a presence of centralised hubs in a network to which lower degree nodes connect. It may also be a sign of a high proportion of isolated nodes

Freeman degree centralisation

Freeman degree centralisation quantifies the relative dominance of the highest degree actor in a network. Hub and spoke networks that centre around a single focal point display high Freeman centralisation. The theoretical Freeman degree centralisation maximum would be reached in a hypothetical case of a perfect star diagram in which one of UCRH’s co-authoring organisations was connected to every organisation in the sample through a separate publication, and all the other organisations never co-authored together during the period. In practice, it is relatively easier to get closer to this hypothetical state in smaller networks

Density

Network density is the proportion of the actual number of connections to the theoretically possible maximum number in a network (which is given by the network size defined as the number of its nodes). The possible connections among a set of nodes increases quadratically with the number of nodes. Therefore, density is expected to be lower in large networks with generally similar levels of networking activity expressed by mean degree

Components

Components of a network are network parts that are disconnected from one another. There is a path between all pairs of nodes in the same component and no network path between separate components. The number of disjoint components in a network is a measure of its fragmentation. A fully connected network has only one component that all nodes belong to. An isolated node with no connections is a component of size one

Network diameter

The diameter of the network is the shortest distance between its two most distant nodes. It is measured by the maximum number of edges needed to connect any two nodes in the network

Assortativity

Assortativity is the tendency of nodes being connected to similar nodes in the network. Assortativity values for a certain node characteristic can vary from -1 to + 1, with negative values indicating the prevalence of links between dissimilar nodes, positive values indicating a prevalence of links between similar nodes, and zero in absolute value indicating a non-assortative network [37]. The magnitude of assortativity co-efficients are interpreted in the same way as correlation co-efficients