Research projects are primarily collaborative in nature through internal and external partnerships, but what role does funding play in their formation? Here, we examined over 43,000 funded projects in the past three decades, enabling us to characteri
se changes in the funding landscape and their impacts on the underlying collaboration patterns. We observed rising inequality in the distribution of funding and its effect was most noticeable at the institutional level in which the leading universities diversified their collaborations and increasingly became the knowledge brokers. Furthermore, these universities formed a cohesive core through their close ties, and such reliance appeared to be a key for their research success, with the elites in the core over-attracting resources but in turn rewarding in both research breadth and depth. Our results reveal how collaboration networks undergo previously unknown adaptive organisation in response to external driving forces, which can have far-reaching implications for future policy.
Ensembles of networks are used as null-models to discriminate network structures. We present an efficient algorithm, based on the maximal entropy method to generate network ensembles defined by the degree sequence and the rich-club coefficient. The m
ethod is applicable for unweighted, undirected networks. The ensembles are used to generate correlated and uncorrelated null--models of a real networks. These ensembles can be used to define the partition of a network into soft communities.
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social networks
where people are involved in different types of relationships and interact through various forms of communication media. The ranking of nodes in multiplex networks is one of the most pressing and challenging tasks that research on complex networks is currently facing. When pairs of nodes can be connected through multiple links and in multiple layers, the ranking of nodes should necessarily reflect the importance of nodes in one layer as well as their importance in other interdependent layers. In this paper, we draw on the idea of biased random walks to define the Multiplex PageRank centrality measure in which the effects of the interplay between networks on the centrality of nodes are directly taken into account. In particular, depending on the intensity of the interaction between layers, we define the Additive, Multiplicative, Combined, and Neutr
