Are Oriented Graphs Related to Oriented Matroids? My professor said that oriented matroids make it easier to investigate things such as connectivity. Recall that an oriented graph is a digraph without multiple edges or loops. Now
Are oriented graphs related to oriented matroids? Or does the term orientation here mean something totally distinct things?


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*Where can you find analysis on the relationship between the two concepts with orientations in graphs and matroids?

*What are good introductory material on matroid with background in graph theory? 
 A: Just as undirected graphs give rise to so called graphic matroids, directed graphs give rise to graphic oriented matroids. Here's the set up:
A directed graph $G = (V,E,\mathcal{O})$ (possibly with loops and/or multiple edges) with orientation $\mathcal{O}$ has associated to it an oriented matroid called the graphic oriented matroid of $M(G)$ of $G$. The oriented matroid $M(G)$ is a representable oriented matroid represented by the signed vertex-edge incidence matrix $N(G)$ of $G$ defined as follows. $N(G)$ has rows (respectively, columns) indexed by the vertices (resp. edges) of $G$. The entry $(v,e)$ of $N$ is given by
$$ N(v,e) = 
\begin{cases}
1 &\text{ if $v$ is the head of the edge $e$},\\
-1 &\text{ if $v$ is the tail of the edge $e$},\\
0 &\text{otherwise}.
\end{cases}$$
While all graphic matroids are orientable, this is not the case for general matroids. For example, the Fano matroid is not orientable. Oxley's Matroid Theory provides a brief discussion on orientable matroids and is easily accessible for anyone with a basic background in graph theory. The standard text for oriented matroids, Oriented Matroids, also discusses the interplay between oriented matroids and (non)orientable matroids.
