Abstract
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated and derive analytic formulas for the joint nearest-neighbor degree probability distribution. Using those results we describe correlations in maximal entropy connected random graphs. We show that connected graphs are disassortative and that correlations are strongly related to the presence of one-degree nodes (leaves). We propose an efficient algorithm for generating connected random graphs. We illustrate our results with several examples.
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.
