Abstract
This paper introduces the notions of chained and semi-chained graphs. The chain of a graph, when existent, refines the notion of bipartivity and conveys important structural information. Also the notion of a center vertex v_c is introduced. It is a vertex, whose sum of p powers of distances to all other vertices in the graph is minimal, where the distance between a pair of vertices {v_c,v} is measured by the minimal number of edges that have to be traversed to go from v_c to v. This concept extends the definition of closeness centrality. Applications in which the center node is important include information transmission and city planning. Algorithms for the identification of approximate central nodes are provided and computed examples are presented.
Highlights
Complex systems are made up of a collection of objects, that are connected to each other in some manner, and can be modeled as networks
This paper introduces the notions of chained and semi-chained graphs
Networks can be applied to model systems that arise in social science, telecommunication, transportation, as well as in many other areas; see, e.g., Estrada (2011a), Estrada and Knight (2015), and Newman (2010) for discussions on networks and for many examples of their applications
Summary
Complex systems are made up of a collection of objects, that are connected to each other in some manner, and can be modeled as networks.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
