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.