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In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). 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 ...
A simple unweighted network of size is called sparse if the number of links in it is much smaller than the maximum possible number of links : [1] = (). In any given (real) network, the number of nodes N and links M are just two numbers, therefore the meaning of the much smaller sign (above) is purely colloquial and informal, and so are statements like "many real networks are sparse."
Sparse mode assumes relatively fewer receivers. Dense mode is ideal for groups where many of the nodes will subscribe to receive the multicast packets, so that most of the routers must receive and forward these packets (groups of a high density). This difference shows up in the initial behavior and mechanisms of the two protocols.
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1] There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of ...
The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory. The adjacency matrix of a graph should be distinguished from its incidence matrix , a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix ...
In mathematics, a sparse polynomial (also lacunary polynomial [1] or fewnomial) [2] is a polynomial that has far fewer terms than its degree and number of variables would suggest. For example, x 10 + 3 x 3 + 1 {\displaystyle x^{10}+3x^{3}+1} is a sparse polynomial as it is a trinomial with a degree of 10 {\displaystyle 10} .
The Eigen library supplies Cholesky factorizations for both sparse and dense matrices. In the ROOT package, the TDecompChol class is available. In Analytica, the function Decompose gives the Cholesky decomposition. The Apache Commons Math library has an implementation which can be used in Java, Scala and any other JVM language.
The sparse code is when each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons. In contrast to sensor-sparse coding, sensor-dense coding implies that all information from possible sensor locations is known.