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The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The first and second Zagreb indices for a graph with vertex count n and vertex degrees v_i for i=1, ..., n are defined by Z_1=sum_(i=1)^nv_i^2 and Z_2=sum_((i,j) in ...

The Q-chromatic polynomial, introduced by Birkhoff and Lewis (1946) and termed the "Q-chromial" by Bari (1974), is an alternate form of the chromatic polynomial pi(x) defined ...

A snark on 30 vertices with edge chromatic number 4. It is implemented in the Wolfram Language as GraphData["DoubleStarSnark"].

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...

A 2-dimensional discrete percolation model is said to be mixed if both graph vertices and graph edges may be "blocked" from allowing fluid flow (i.e., closed in the sense of ...