* The formation of clusters of linked nodes in a network, measured by the clustering coefficient.

Graph theory also offers a context-free measure of connectedness, called the clustering coefficient.

Another important characteristic of scale-free networks is the clustering coefficient distribution, which decreases as the node degree increases.

Similarly, the clustering coefficient of scale-free networks can vary significantly depending on other topological details.

A higher clustering coefficient indicates a greater ' cliquishness '.

They noted that graphs could be classified according to two independent structural features, namely the clustering coefficient, and average node-to-node distance ( also known as average shortest path length ).

Purely random graphs, built according to the Erdős – Rényi ( ER ) model, exhibit a small average shortest path length ( varying typically as the logarithm of the number of nodes ) along with a small clustering coefficient.

Watts and Strogatz measured that in fact many real-world networks have a small average shortest path length, but also a clustering coefficient significantly higher than expected by random chance.

Watts and Strogatz then proposed a novel graph model, currently named the Watts and Strogatz model, with ( i ) a small average shortest path length, and ( ii ) a large clustering coefficient.

This follows from the defining property of a high clustering coefficient.

In a power law distributed small world network, deletion of a random node rarely causes a dramatic increase in mean-shortest path length ( or a dramatic decrease in the clustering coefficient ).

In graph theory, a clustering coefficient is a measure of degree to which nodes in a graph tend to cluster together.

The global clustering coefficient is based on triplets of nodes.

The global clustering coefficient is the number of closed triplets ( or 3 x triangles ) over the total number of triplets ( both open and closed ).

Example local clustering coefficient on an undirected graph.

The local clustering coefficient of the blue node is computed as the proportion of connections among its neighbors which are actually realized compared with the number of all possible connections.

In the top part of the figure all three possible connections are realised ( thick black segments ), giving a local clustering coefficient of 1.

Finally, none of the possible connections among the neighbours of the blue node are realised, producing a local clustering coefficient value of 0.

The local clustering coefficient of a vertex ( node ) in a graph quantifies how close its neighbors are to being a clique ( complete graph ).

The local clustering coefficient for a vertex is then given by the proportion of links between the vertices within its neighbourhood divided by the number of links that could possibly exist between them.

Thus, the local clustering coefficient for directed graphs is given as

Thus, the local clustering coefficient for undirected graphs can be defined as

Then we can also define the clustering coefficient as

The clustering coefficient for the whole network is given by Watts and Strogatz as the average of the local clustering coefficients of all the vertices:

An advantage of being exposed to such specificity about an important and recurring feature of social reality is that it can be taken advantage of by the reader to examine covert as well as overt resonances within himself, resonances triggered by explicit symbols clustering around the central figure of the Jew.

There is strong observational evidence for dark energy, as the total energy density of the universe is known through constraints on the flatness of the universe, but the amount of clustering matter is tightly measured, and is much less than this.

Apart from its density and its clustering properties, nothing is known about dark energy.

In a relational database clustering the two respective relations " Items " and " Orders " results in saving the expensive execution of a Join operation between the two relations whenever such a join is needed in a query ( the join result is already ready in storage by the clustering, available to be utilized ).

The simplest model for this that is in general agreement with observed phenomena is the Cold Dark Matter cosmology ; that is to say that clustering and merging is how galaxies gain in mass, and can also determine their shape and structure.

The representativeness heuristic is also cited behind the related phenomenon of the clustering illusion, according to which people see streaks of random events as being non-random when such streaks are actually much more likely to occur in small samples than people expect.

The new loop may also be passed between two stitches in the present row, thus clustering the intervening stitches ; this approach is often used to produce a smocking effect in the fabric.

The reliability is provided through single-system quality and self-healing, and in multi-system installations, clustering technology and application failover on a system outage, as well as error monitoring and correction.

Another central design philosophy is support for extremely high quality of service ( QoS ), even within a single operating system instance, although z / OS has built-in support for Parallel Sysplex clustering.

The idea behind this GA evolution proposed by Emanuel Falkenauer is that solving some complex problems, a. k. a. clustering or partitioning problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes.

; Instruction scheduling: Instruction scheduling is an important optimization for modern pipelined processors, which avoids stalls or bubbles in the pipeline by clustering instructions with no dependencies together, while being careful to preserve the original semantics.

Each group is represented by its centroid point, as in k-means and some other clustering algorithms.

What is the explanation for this clustering?

Conceptual clustering is a modern variation of the classical approach, and derives from attempts to explain how knowledge is represented.

It is distinguished from ordinary data clustering by generating a concept description for each generated category.

Different clustering techniques make different assumptions on the structure of the data, often defined by some similarity metric and evaluated for example by internal compactness ( similarity between members of the same cluster ) and separation between different clusters.

In most methods of hierarchical clustering, this is achieved by use of an appropriate metric ( a measure of distance between pairs of observations ), and a linkage criterion which specifies the dissimilarity of sets as a function of the pairwise distances of observations in the sets.

One way of clustering a set of data points in a metric space into two clusters is to choose the clusters in such a way as to minimize the sum of the diameters of the clusters, where the diameter of any single cluster is the largest distance between any two of its points ; this is preferable to minimizing the maximum cluster size, which may lead to very similar points being assigned to different clusters.

For a clustering example, suppose this data is to be clustered using Euclidean distance as the distance metric.

There is a real danger that the combination of " Tanimoto Distance " being defined using this formula, along with the statement " Tanimoto Distance is a proper distance metric " will lead to the false conclusion that the function is in fact a distance metric over vectors or multisets in general, whereas its use in similarity search or clustering algorithms may fail to produce correct results.