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Gavin (41) [Avatar] Offline
In Software engineering, the head is the first item in a collection, the tail is everything else (after the head).

for the following;

Vi is called the tail, or start node, and Vj is called head, or end node.

this seems wrong, upon initial reading.

Perhaps you could add some words about how an edge can often be visualised as an arrow - and so the tail / head of the arrow , aids in the mental image of tail / head "ends" for a graph?
Alessandro Negro (11) [Avatar] Offline
There is no error there. The entire sentence is:

In directed graphs an edge can Eij can be traversed from Vi to Vj but not in the opposite direction; Vi is called the tail, or start node, and Vj is called head, or end node.

From the sentence it is clear that we are talking about a directed graph and so about directed edges (the arrow you were talking about is related to the visualization, it is not a mathematical or formal concept). In a directed edge from Vi to Vj, by definition, the first node is called start node or tail while the second one is called end node or head. This is a pure graph formalism nothing related to software development or similar. Graph theory exists much before than the first ever line of code smilie
Gavin (41) [Avatar] Offline
Hi again...

Let me first say - that I totally agree with you.
Graph theory and software engineering are not the same thing.

Let's assume I know nothing of Category or Graph theory.
Let's also assume that I have your book because I am software developer and want to learn about AI and Graph Dbs and how I might utilise them together in my projects.
Which is the premise of the book

From the perspective of the reader - when I first come across your sentence;
Vi is called the tail, or start node, and Vj is called head, or end node.

I think "you" have made a mistake and inverted, what you meant to say.
it isn't initially clear to me - that Graph / Category theory, uses the same words I am used to in software engineering - in the directly opposite meaning.

Subsequently, a sentence that clarifies, what you have written is correct / how it is different to my software engineering assumption, could be useful here.
Especially since this is the start of the book - and I'm not necessarily fully "in" your graph world, yet.

(and again let me say that all of these things are just suggestions - I sincerely don't take it personally if you disagree with me. After all it is your book smilie )