How is an $O$-graph different from a directed graph? - Category Theory I'm reading Category Theory by Mac Lane and I'm trying to understand the paragraphs in the pictures included below.
What is the difference between a directed graph and an $O$-graph?
Why is the picture in the blue box considered an $O$-graph? 
The blue box picture looks like two parallel morphisms between two digraphs both called $O$, and not an $O$-graph which is defined as a single digraph.  
What does it mean by both functions domain and range the identity?


 A: 
What is the difference between a directed graph and an $O$−graph?

An $O$-graph is a directed graph where $O$ is the set of vertices (although the category of $O$-graphs differs substantially from the category of directed graphs—see Alex Kruckman's comment below). For example, this graph (public domain image from Wikimedia Commons, created by Wikimedia user     Booyabazooka) is a $\{1, 2, 3, 4\}$-graph: 
 

Why is the picture in the blue box considered an $O$−graph?

The way MacLane defines a graph is as four pieces of information:


*

*A set $A$ of arrows

*A set $O$ of verticies

*A function $\partial_0: A \rightarrow O$, which defines the tail of each arrow

*A function $\partial_1: A \rightarrow O$, which defines the head of each arrow


For example, for the graph in the image above:


*

*$A$ is a set with 6 elements, which could be $\{e_1, e_2, \dots, e_6\}$.

*$O = \{1, 2, 3, 4\}$

*If $e_1$ is the top horizontal arrow from $1$ to $2$, then $\partial_0(e_1) = 1$ and $\partial_1(e_1) = 2$.


MacLane uses the shorthand $A \rightrightarrows O$ for the two functions $\partial_0: A \rightarrow O$ and $\partial_1: A \rightarrow O$. 
The graph $O \rightrightarrows O$ means a graph where each element of $O$ is regarded as both a vertex and an arrow. By saying that $\partial_0$ and $\partial_1$ are both identity functions, he's saying that each element of $x \in O$, when regarded as an arrow, is a loop from the vertex $x$ to itself. 
A: The directed graph has $A$ for arrows and $O$ for vertices. The $O$-graph has $O$ for its vertices. The $O$ just seems to be an explicit mention of the underlying set, whereas a graph can have any set of vertices.
I believe that they mean that the "simplest example" of an $O$-graph is the one where both of the arrows $O\to O$ are the identity.
