Connectivity of a Family of Bilateral Agreement Random Graphs
Hossein Dabirian, Vijay Subramanian

TL;DR
This paper proves La and Kabkab's conjecture that connectivity in bilateral agreement random graphs occurs when the parameter exceeds a threshold of 1, and introduces an asymptotic for the average degree of these graphs.
Contribution
The paper provides a proof for the conjectured connectivity threshold in bilateral agreement random graphs and derives an asymptotic expression for their average degree.
Findings
Connectivity occurs at t>1 with high probability.
Graph is disconnected for t<1.
Derived asymptotic for average degree.
Abstract
Bilateral agreement based random undirected graphs were introduced and analyzed by La and Kabkab in 2015. The construction of the graph with vertices in this model uses a (random) preference order on other vertices and each vertex only prefers the top other vertices using its own preference order; in general, can be a function of . An edge is constructed in the ensuing graph if and only if both vertices of a potential edge prefer each other. This random graph is a generalization of the random -nearest neighbor graphs of Cooper and Frieze that only consider unilateral preferences of the vertices. Moharrami \emph{et al.} studied the emergence of a giant component and its size in this new random graph family in the limit of going to infinity when is finite. Connectivity properties of this random graph family have not yet been formally analyzed. In their…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic
