Consider a Erdős–Rényi graph on $n$ nodes, say $1,2,\ldots,n$, ($n\geq 3$) such that the probability of edge between any two nodes is $c/n$. I wish to know if there is a result tha …

suppose nodes with radius R are distributed randomly in Area of size A, then how can we calculate the degree of each node by geometric random graph.

It is well-known that a random graph a.e. has diameter 2. It is also well-known that the number of distinct eigenvalues of a graph is at least the diameter plus one. But what is k …

Background and definitions Consider a random graph on $n$ vertices with a nicely behaved degree sequence. That is, letting $d_i(n)$ denote the number of vertices of degree $i$, s …

Imagine one generates some form of random graph (e.g. a random geometric graph) and via simulation, calculates the probability that there exists an edge-wise path between all verti …

Imagine I cover an arbitrarily large plane with randomly placed points at some density $\rho$ s.t. the number of points in any randomly sampled area $A$ (of arbitrary shape and siz …

Imagine I form a random graph by simulating random sequential adsorption (RSA) of discs (each with the same radius $r$) on $[0,1]^2$ until I cover the plane at a density $\leq U$, …

There are two or more ways to define an Erdos-Rényi random graph. Let consider the following two: 1) $G_n=(V_n,E_n)$ with vertex set $V_n=(1,\dots,n)$ and edge set $E_n=(ij\in\mat …

consider the set of graphs with $n$ vertices and exactly half of all $\binom n 2$ possible edges. looking for a formula that counts the number of these graphs that have a $k$- …

i read a note talking about this fact, bipartite graphs are rare in regular graphs. but it do not state how rare it is? just curious about it. thank you very much.

A question I asked at math.SE without elliciting an answer. Let $G(n,p)$ be an Erdős–Rényi graph on $n$ vertices. Is there an explicit expression for the probability $P_{n,p}(u,v) …

Suppose you take a $G(n,p)$ random graph for a fixed probability $p$ and find a spanning tree using Kruskal's algorithm. If you now repeat this process indefinitely, will every tre …

The theory of random graphs, after the pioneering classic work of Erdős & Rényi, has come to prominence with many further refinements, most notably the small world theory (Bar …

This is a request for reference. Where can I find discussion of the Erdős–Rényi random graph in the regime between "giant-component" and "fully connected"? e.g. a detailed picture …

In the study of biological neural networks, researchers sometimes compare hypotheses vs. a degree-preserving random null model. One major criticism against this approach is that c …