Abstract
New betweenness centralities of nodes in a directed network are proposed based on the idea that nodes in a network are processes rather than things. They are called input and output betweenness centralities. They measure importance of nodes as input and output for gluing arcs together as interface between processes, respectively. We demonstrate their use and discuss their meaning by calculating them in two toy directed networks and one real-world network. We also compare them with the existing centrality measures that reflect asymmetry of links in directed networks: out- and in-degrees and Hub and Authority scores. We found that input and output betweenness centralities behave differently from these measures in some nodes. It is suggested that they can effectively identify nodes that are less important in terms of existing measures but are noteworthy from the viewpoint that nodes are processes.
Highlights
Categorical network theory is a general framework to study open networks, namely, networks with explicit input and output nodes such as electrical circuits (Baez and Fong 2015), signal flow diagrams (Baez and Erbele 2015; Bonchi et al 2014) and chemical reaction networks (Baez and Pollard 2017)
The primary interest of categorical network theory is the behavior of open networks determined by the relation between inputs and outputs that is revealed by black-boxing the internal structure of networks (Baez and Fong 2015)
Based on the category theoretic representation of this viewpoint, we proposed betweenness centralities of nodes as input and output called input betweenness centrality (IBC) and output betweenness centrality (OBC), respectively
Summary
Categorical network theory is a general framework to study open networks, namely, networks with explicit input and output nodes such as electrical circuits (Baez and Fong 2015), signal flow diagrams (Baez and Erbele 2015; Bonchi et al 2014) and chemical reaction networks (Baez and Pollard 2017). It thinks of networks as processes in contrast to network science where networks are thought of as things (Baez 2014). The divide into networks as things and networks as processes is a natural consequence of the category theoretic perspective.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
