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The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
The density of the maximally dense subgraph of a graph is sometimes referred to as its subgraph density. A subgraph with maximal density can also be seen as a subgraph with maximal average degree in the graph. Subgraph density is asymptotic to the related notion of arboricity and to graph degeneracy.
In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve). Main article: Central limit theorem The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution.
The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently. An alternative to kernel density estimation is the average shifted histogram, [8] which is fast to compute and gives a smooth curve estimate of the density without using kernels.
The algorithm for computing a dot plot is closely related to kernel density estimation. The size chosen for the dots affects the appearance of the plot. Choice of dot size is equivalent to choosing the bandwidth for a kernel density estimate. In the R programming language this type of plot is also referred to as a stripchart [3] or stripplot. [4]
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