TITLE: Are these two graphs isomorphic? Why/Why not?
QUESTION [12 upvotes]: Are these two graphs isomorphic?


According to Bruce Schneier:

"A graph is a network of lines connecting different points. If two graphs are identical except for the names of the points, they are called isomorphic."

Schneier, B.  "Graph Isomorphism"
From Applied Cryptography
John Wiley & Sons Inc.
ISBN 9780471117094


According to a GeeksforGeeks article:
These two are isomorphic:

And these two aren't isomorphic:

Manwani, C. "Graph Isomorphisms and Connectivity"
From GeeksforGeeks
https://www.geeksforgeeks.org/mathematics-graph-isomorphisms-connectivity/

According to a MathWorld article:

"Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic."

Weisstein, Eric W. "Isomorphic Graphs."
From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/IsomorphicGraphs.html

The details are beyond me, but the MathWorld explanation seems to conflict with the first GeeksforGeeks example; the vertices appear the same, but they appear to be connected differently.  
To add to the confusion, the same could be said for the second example. So I can't really deduce the facts.
Please try to keep answers as clear and simple as possible for the sake of understanding.

"Truth is ever to be found in the simplicity, and not in the
  multiplicity and confusion of things." 
–Isaac Newton

REPLY [10 votes]: Disclaimer
This answer is an excuse to show an animation that a 5-year-old might understand.
If you're looking for correct mathematical definitions, please switch to other answers or Wikipedia.
Definitions
First, please be careful not to confuse:

a graph and the representation of a graph
a graph and a chart.

Isomorphism
In layman terms, two graphs are isomorph if there is a continuous movie transforming the representation of a graph into the other:

It is allowed to drag and rename vertices, it is not allowed to add or cut edges. The movie acts as an edge-preserving bijection, which is how graph isomorphism can be defined.
Here's the online tool I used.
Non-Isomorphism
The second example is here.
By dragging around vertices, you cannot create the triangles ($b,c,d$ or $a,e,f$) that are present in the other graph:

From a logical point of view, it isn't enough to show one failed attempt in order to prove that something isn't possible. To prove that the graphs aren't isomorph, you could count their cliques.