I started to dive into the topic "Knowledge Graph" and I get the feeling that this is the same as the "Linked Open Data". I have some questions 1) If so, why did they need to invent a new concept. 2) If not, what is the difference and what does ontology have to do with it? 3) And how all this is connected with neural networks?

I hope the answers to these questions can clarify the concepts and point the way.

Linked Open Data vs Knowledge Graphs

So the Linked Open Data (LOD) movement generally refers to the concept of publishing open data using semantic web standards i.e. Resource Description Framework (RDF). These datasets are typically published by multiple parties (researchers, corporations, individuals) and may vary in quality wildly. Despite the name they may not necessarily be linked at all, while the LOD movement encourages reusing identifiers and linking to pre-existing datasets this is not a requirement so the quality and quantity of linkages varies a lot. See the diagram on the linked LOD wikipedia page for an overview of which datasets link to where.

Knowledge Graphs (KGs) are broadly speaking a rebranding of LOD but in practise tend to have several differences. From a business perspective it's often much easier for people to make the case for an internal KG project than a LOD project. As proposing a LOD project inevitably leads to questions about whether you're giving away your intellectual property. This leads to the first difference, KGs typically aren't open, they are built for a specific organisation or application domain and usually kept propriety. Secondly, the linking may, depending on the KG, only be internal to that KG, or it may link out to relevant LOD elsewhere.

The other major difference is that a KG need not be built with semantic web standards, its perfectly possible (and quite normal) to build a KG using Labelled Property Graphs (LPG). Depending on the use case for the KG the choice of RDF vs LPG data model may fall out naturally from how it will be used. Of course there are systems like Amazon Neptune that let you combine both worlds if the use cases are varied.

What's Ontology got to do with it?

Ontologies are just formal representations of your data schema. RDF has more formalised standards around this, such as RDFS and OWL, but an ontology is broadly equivalent to a schema in traditional database terminology.

Any LOD or KG project is going to involve some kind of Ontology, or Data Schema, as without that they tend to be fairly unusable i.e. if your data doesn't have some structure to it it's hard to build anything useful atop it.

And what about neural networks?

Neural Networks are a concept from Artificial Intelligence research and doesn't really have any direct connection to LOD and KGs.

That being said a LOD or KG project could be used as part of the training data for a neural network but what that looks like it would be very use case specific.