If a graph G has e edges, v vertices, and p components, the rank of G, written ρ(G), is defined to be v – p
The nullity of G, written μ(G), is e – v + p Thus ρ(G) + μ(G) = e
With reference to a directed graph, a weakly connected graph is one in which the direction of each edge must be removed before the graph can be connected in the manner described above. If however there is a directed path between each pair of vertices u and v and another directed path from v back to u, the directed graph is strongly connected.
More formally, let G be a directed graph with vertices V and edges E. The set V can be partitioned into equivalence classes V1, V2,… under the relation that vertices u and v are equivalent iff there is a path from u to v and another from v to u. Let E1, E2,… be the sets of edges connecting vertices within V1, V2,… Then each of the graphs Gi with vertices Vi and edges Ei is a strongly connected component of G. A strongly connected graph has precisely one strongly connected component.
The process of replacing each of the strongly connected components of a directed graph by a single vertex is known as condensation.
"connected graph." A Dictionary of Computing. . Encyclopedia.com. (October 23, 2017). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/connected-graph
"connected graph." A Dictionary of Computing. . Retrieved October 23, 2017 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/connected-graph
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.