- - graph.
- - directed graph
- - vertex set (of )
- - edge set (of )
- - arc set of directed graph .
- - adjacency relation
- - edge
- - generic edge.
- - generic vertex
- - weight of edge in weighted graph.
- - usually denotes the size of the vertex set.
- - usually denotes the size of the edge / arc set.
- - usually denotes the number of components.
- - adjacency matrix of
- - incidence matrix of
- - degree matrix of
- - Laplacian matrix of
- - edge Laplacian matrix of .
- - weight matrix of
- - weight of the weighted graph .
- - is isomorphic to
- - is a subgraph of .
- - is a proper subgraph of .
- - induced subgraph on the set
- - complement of the graph.
- - union of two graphs
- - intersection of two graphs.
- - boundary of the induced subgraph .
- - closure of
- - sum of graphs.
- - oriented graph. Specifically is strongly oriented (or such an orientation is defined)
- - the Cartesian product of and .
- - null graph on vertices.
- - complete graph on vertices.
- - complete bipartite graph.
- - path of vertices
- - cycle of vertices
- - generic cycle
- - generic cut-set related to cycle
- - edge addition, assuming is an edge set
- - edge contraction.
- - edge deletion, assuming is an edge set
- - vertex deletion, assuming is a vertex set
- - degree of vertex
- - minimum degree of .
- - maximum degree of .
- - indegree of vertex
- - outdegree of vertex
- - neighborhood of vertex or vertex set .
- - density of .
- - number of components of
- - vertex connectivity of .
- - edge connectivity of
- - generic tree.
- - cotree.
- - cut-set rank
- - cycle rank
- - number of spanning trees in .
- - the set of all spanning trees rooted in . For digraphs, defaults to arborescences.
- - algebraic dual
- - crossing number
- - genus
- - thickness
- - chromatic polynomial
- - chromatic number
- - chromatic index.
- - distance between and .
- - diameter of the graph
- - betweenness centrality of edge .
- - link betweenness centrality of edge
- - clustering coefficient of vertex
- - in flow networks, denotes flow or pseudoflow (default is flow)
- - in flow networks, denotes capacity
- - denotes the value of a flow
- - source vertex
- - sink vertex
- - the topological overlap matrix between vertices and
- - the number of edges needed to separate .
- - the second eigenvalue in assuming eigenvalues are ordered in ascending order.
- - conductance of .
- - isoperimetric number
- - generic automorphism
- - a partition of .
- - cardinality of a partition
- - a quotient of over
- - characteristic vector of cell
- - characteristic matrix