## What is a uniform random graph?

The uniform distribution is a continuous distribution that assigns only positive probabilities within a specified interval (a, b) — that is, all values between a and b. As a result, the graph that illustrates this distribution is a rectangle. The figure shows the uniform distribution defined over the interval (0, 10).

What are key characteristics of random graphs?

has a perfect matching. In particular, the moment the last isolated vertex vanishes in almost every random graph, the graph becomes connected. edges and with probability close to 1 ensures that the graph has a complete matching, with exception of at most one vertex. edges is Hamiltonian.

### What is Δ G graph theory?

Δ(G) (using the Greek letter delta) is the maximum degree of a vertex in G, and δ(G) is the minimum degree; see degree. That is, it is the maximum of the distances between pairs of vertices in the graph.

What does a uniform distribution graph look like?

The uniform distribution can be visualized as a straight horizontal line, so for a coin flip returning a head or tail, both have a probability p = 0.50 and would be depicted by a line from the y-axis at 0.50.

#### What are random networks?

A random network consists of N nodes where each node pair is connect- ed with probability p. 2) Select a node pair and generate a random number between 0 and 1. If the number exceeds p, connect the selected node pair with a link, otherwise leave them disconnected.

What is the first theorem of graph theory?

The following theorem is often referred to as the First Theorem of Graph The- ory. Theorem 1.1. In a graph G, the sum of the degrees of the vertices is equal to twice the number of edges. Consequently, the number of vertices with odd degree is even.

## What are the 2 requirements of a density curve?

1. The total area under the curve must equal 1. 2. Every point on the curve must have a vertical height that is 0 or greater.