Year: 2014
Type: preprint
Abstract: In this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many applications, and it plays an important role in the web search algorithm of Brin and Page, the foun-dation of the search engine Google. We also show that for this closed model, Euler graphs are particular examples of cofibrant objects. This enables us to interpret in this setting the classical result of Euler which states that a directed graph is Euleurian if and only if the in degree and the out degree of every of its nodes are equal. We also provide a cohomological proof of this last result.
Source: arXiv (Cornell University)
Author: Tsemo, Aristide
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2271876162