Nat  Kutch

Nat Kutch

1596026040

Graph Theory | Introduction to Trees

What’s happening everyone? This is the latest addition to my brand new series Graph Theory: Go Hero where we discuss about graphs and related algorithms, in depth. Check it out for a quick overview. Here we’re going have a light introduction to tree which is a kind of graph. So, here we go.

What is a tree?

Image for post

We have a couple of graphs above, can you spot the odd one out?

Correct, the forth one stands out of the group. But why?

Image for post

Because a tree is an undirected graph with no cycles. The key thing to remember is trees aren’t allowed to have cycles in it. You could find one that broke the rule, right? Excellent job.

However, there’s another simple method which we can use to see whether the given graph is a tree or not. All trees have **N - 1 edges, **where N is the number of nodes.

Image for post

Three of our graphs meet the rule, right? But the last one doesn’t.

Trees out in the wild

Let’s see a couple of occasions where we encounter the applications of trees.

  • File Structure

A computer file system contains directories, subdirectories and files and it’s inherently a tree.

Image for post

  • Corporate Hierarchy

The term corporate hierarchy refers to the arrangement and organization of individuals within a corporation according to power, status, and job function. It delineates authority and responsibility, designating leadership over employees, departments, divisions, and other executives depending on their place within the strata. A complete corporate would have a tree structure.

Image for post

  • Evaluating Mathematical Expressions

Tress could be used to decompose mathematical expressions and source code into an abstract format so that they are evaluated in a formal way. Below is an expression and it’s corresponding tree representation.

(a * b) + (c - d)

Image for post

  • Web Document Object Model (DOM)

Every web page we visit is made of certain tags such as ,

, etc. DOM is an interface that treats and XML or HTML document as a tree structure wherein each node is an object representing a part of the document. One such a tree is given below.</p>

#programming #computer-science #graph-theory #deep learning #deep learning

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Buddha Community

Graph Theory | Introduction to Trees
Nat  Kutch

Nat Kutch

1596026040

Graph Theory | Introduction to Trees

What’s happening everyone? This is the latest addition to my brand new series Graph Theory: Go Hero where we discuss about graphs and related algorithms, in depth. Check it out for a quick overview. Here we’re going have a light introduction to tree which is a kind of graph. So, here we go.

What is a tree?

Image for post

We have a couple of graphs above, can you spot the odd one out?

Correct, the forth one stands out of the group. But why?

Image for post

Because a tree is an undirected graph with no cycles. The key thing to remember is trees aren’t allowed to have cycles in it. You could find one that broke the rule, right? Excellent job.

However, there’s another simple method which we can use to see whether the given graph is a tree or not. All trees have **N - 1 edges, **where N is the number of nodes.

Image for post

Three of our graphs meet the rule, right? But the last one doesn’t.

Trees out in the wild

Let’s see a couple of occasions where we encounter the applications of trees.

  • File Structure

A computer file system contains directories, subdirectories and files and it’s inherently a tree.

Image for post

  • Corporate Hierarchy

The term corporate hierarchy refers to the arrangement and organization of individuals within a corporation according to power, status, and job function. It delineates authority and responsibility, designating leadership over employees, departments, divisions, and other executives depending on their place within the strata. A complete corporate would have a tree structure.

Image for post

  • Evaluating Mathematical Expressions

Tress could be used to decompose mathematical expressions and source code into an abstract format so that they are evaluated in a formal way. Below is an expression and it’s corresponding tree representation.

(a * b) + (c - d)

Image for post

  • Web Document Object Model (DOM)

Every web page we visit is made of certain tags such as ,

, etc. DOM is an interface that treats and XML or HTML document as a tree structure wherein each node is an object representing a part of the document. One such a tree is given below.</p>

#programming #computer-science #graph-theory #deep learning #deep learning

Luna  Mosciski

Luna Mosciski

1595932020

Graph Therapy: The Year of the Graph Newsletter, June/May 2020

Parts of the world are still in lockdown, while others are returning to some semblance of normalcy. Either way, while the last few months have given some things pause, they have boosted others. It seems like developments in the world of Graphs are among those that have been boosted.

An abundance of educational material on all things graph has been prepared and delivered online, and is now freely accessible, with more on the way.

Graph databases have been making progress and announcements, repositioning themselves by a combination of releasing new features, securing additional funds, and entering strategic partnerships.

A key graph database technology, RDF*, which enables compatibility between RDF and property graph databases, is gaining momentum and tool support.

And more cutting edge research combining graph AI and knowledge graphs is seeing the light, too. Buckle up and enjoy some graph therapy.


Stanford’s series of online seminars featured some of the world’s leading experts on all things graph. If you missed it, or if you’d like to have an overview of what was said, you can find summaries for each lecture in this series of posts by Bob Kasenchak and Ahren Lehnert. Videos from the lectures are available here.

Stanford Knowledge Graph Course Not-Quite-Live-Blog

Stanford University’s computer science department is offering a free class on Knowledge Graphs available to the public. Stanford is also making recordings of the class available via the class website.


Another opportunity to get up to speed with educational material: The entire program of the course “Information Service Engineering” at KIT - Karlsruhe Institute of Technology, is delivered online and made freely available on YouTube. It includes topics such as ontology design, knowledge graph programming, basic graph theory, and more.

Information Service Engineering at KIT

Knowledge representation as a prerequisite for knowledge graphs. Learn about knowledge representation, ontologies, RDF(S), OWL, SPARQL, etc.


Ontology may sound like a formal term, while knowledge graph is a more approachable one. But the 2 are related, and so is ontology and AI. Without a consistent, thoughtful approach to developing, applying, evolving an ontology, AI systems lack underpinning that would allow them to be smart enough to make an impact.

The ontology is an investment that will continue to pay off, argue Seth Earley and Josh Bernoff in Harvard Business Review, making the case for how businesses may benefit from a knowldge-centric approach

Is Your Data Infrastructure Ready for AI?

Even after multiple generations of investments and billions of dollars of digital transformations, organizations struggle to use data to improve customer service, reduce costs, and speed the core processes that provide competitive advantage. AI was supposed to help with that.


Besides AI, knowledge graphs have a part to play in the Cloud, too. State is good, and lack of support for Stateful Cloud-native applications is a roadblock for many enterprise use-cases, writes Dave Duggal.

Graph knowledge bases are an old idea now being revisited to model complex, distributed domains. Combining high-level abstraction with Cloud-native design principles offers efficient “Context-as-a-Service” for hydrating stateless services. Graph knowledge-based systems can enable composition of Cloud-native services into event-driven dataflow processes.

Kubernetes also touches upon Organizational Knowledge, and that may be modeled as a Knowledge Graph.

Graph Knowledge Base for Stateful Cloud-Native Applications

Extending graph knowledge bases to model distributed systems creates a new kind of information system, one intentionally designed for today’s IT challenges.


The Enterprise Knowledge Graph Foundation was recently established to define best practices and mature the marketplace for EKG adoption, with a launch webinar on June the 23rd.

The Foundation defines its mission as including adopting semantic standards, developing best practices for accelerated EKG deployment, curating a repository of reusable models and resources, building a mechanism for engagement and shared knowledge, and advancing the business cases for EKG adoption.

Enterprise Knowledge Graph Maturity Model

The Enterprise Knowledge Graph Maturity Model (EKG/MM) is the industry-standard definition of the capabilities required for an enterprise knowledge graph. It establishes standard criteria for measuring progress and sets out the practical questions that all involved stakeholders ask to ensure trust, confidence and usage flexibility of data. Each capability area provides a business summary denoting its importance, a definition of the added value from semantic standards and scoring criteria based on five levels of defined maturity.


Enterprise Knowledge Graphs is what the Semantic Web Company (SWC) and Ontotext have been about for a long time, too. Two of the vendors in this space that have been around for the longer time just announced a strategic partnership: Ontotext, a graph database and platform provider, meets SWC, a management and added value layer that sits on top.

SWC and Ontotext CEOs emphasize how their portfolios are complementary, while the press release states that the companies have implemented a seamless integration of the PoolParty Semantic Suite™ v.8 with the GraphDB™ and Ontotext Platform, which offers benefits for many use cases.

#database #artificial intelligence #graph databases #rdf #graph analytics #knowledge graph #graph technology

Ruth  Nabimanya

Ruth Nabimanya

1621327800

Graphs and Knowledge Connexions. The Year of the Graph Newsletter, Autumn 2020

As 2020 is coming to an end, let’s see it off in style. Our journey in the world of Graph Analytics, Graph Databases, Knowledge Graphs and Graph AI culminate.

The representation of the relationships among data, information, knowledge and --ultimately-- wisdom, known as the data pyramid, has long been part of the language of information science. Digital transformation has made this relevant beyond the confines of information science. COVID-19 has brought years’ worth of digital transformation in just a few short months.

In this new knowledge-based digital world, encoding and making use of business and operational knowledge is the key to making progress and staying competitive. So how do we go from data to information, and from information to knowledge? This is the key question Knowledge Connexions aims to address.

Graphs in all shapes and forms are a key part of this.


Knowledge Connexions is a visionary event featuring a rich array of technological building blocks to support the transition to a knowledge-based economy: Connecting data, people and ideas, building a global knowledge ecosystem.

The Year of the Graph will be there, in the workshop “From databases to platforms: the evolution of Graph databases”. George Anadiotis, Alan Morrison, Steve Sarsfield, Juan Sequeda and Steven Xi bring many years of expertise in the domain, and will analyze Graph Databases from all possible angles.

This is the first step in the relaunch of the Year of the Graph Database Report. Year of the Graph Newsletter subscribers just got a 25% discount code. To be always in the know, subscribe to the newsletter, and follow the newly launched Year of the Graph account on Twitter! In addition to getting the famous YotG news stream every day, you will also get a 25% discount code.

#database #machine learning #artificial intelligence #data science #graph databases #graph algorithms #graph analytics #emerging technologies #knowledge graphs #semantic technologies

Luna  Mosciski

Luna Mosciski

1595924640

Graph Therapy: The Year of the Graph Newsletter, June/May 2020

Parts of the world are still in lockdown, while others are returning to some semblance of normalcy. Either way, while the last few months have given some things pause, they have boosted others. It seems like developments in the world of Graphs are among those that have been boosted.

An abundance of educational material on all things graph has been prepared and delivered online, and is now freely accessible, with more on the way.

Graph databases have been making progress and announcements, repositioning themselves by a combination of releasing new features, securing additional funds, and entering strategic partnerships.

A key graph database technology, RDF*, which enables compatibility between RDF and property graph databases, is gaining momentum and tool support.

And more cutting edge research combining graph AI and knowledge graphs is seeing the light, too. Buckle up and enjoy some graph therapy.


Stanford’s series of online seminars featured some of the world’s leading experts on all things graph. If you missed it, or if you’d like to have an overview of what was said, you can find summaries for each lecture in this series of posts by Bob Kasenchak and Ahren Lehnert. Videos from the lectures are available here.

Stanford Knowledge Graph Course Not-Quite-Live-Blog

Stanford University’s computer science department is offering a free class on Knowledge Graphs available to the public. Stanford is also making recordings of the class available via the class website.


Another opportunity to get up to speed with educational material: The entire program of the course “Information Service Engineering” at KIT - Karlsruhe Institute of Technology, is delivered online and made freely available on YouTube. It includes topics such as ontology design, knowledge graph programming, basic graph theory, and more.

Information Service Engineering at KIT

Knowledge representation as a prerequisite for knowledge graphs. Learn about knowledge representation, ontologies, RDF(S), OWL, SPARQL, etc.


Ontology may sound like a formal term, while knowledge graph is a more approachable one. But the 2 are related, and so is ontology and AI. Without a consistent, thoughtful approach to developing, applying, evolving an ontology, AI systems lack underpinning that would allow them to be smart enough to make an impact.

The ontology is an investment that will continue to pay off, argue Seth Earley and Josh Bernoff in Harvard Business Review, making the case for how businesses may benefit from a knowldge-centric approach

Is Your Data Infrastructure Ready for AI?

Even after multiple generations of investments and billions of dollars of digital transformations, organizations struggle to use data to improve customer service, reduce costs, and speed the core processes that provide competitive advantage. AI was supposed to help with that.


Besides AI, knowledge graphs have a part to play in the Cloud, too. State is good, and lack of support for Stateful Cloud-native applications is a roadblock for many enterprise use-cases, writes Dave Duggal.

Graph knowledge bases are an old idea now being revisited to model complex, distributed domains. Combining high-level abstraction with Cloud-native design principles offers efficient “Context-as-a-Service” for hydrating stateless services. Graph knowledge-based systems can enable composition of Cloud-native services into event-driven dataflow processes.

Kubernetes also touches upon Organizational Knowledge, and that may be modeled as a Knowledge Graph.

Graph Knowledge Base for Stateful Cloud-Native Applications

Extending graph knowledge bases to model distributed systems creates a new kind of information system, one intentionally designed for today’s IT challenges.


The Enterprise Knowledge Graph Foundation was recently established to define best practices and mature the marketplace for EKG adoption, with a launch webinar on June the 23rd.

The Foundation defines its mission as including adopting semantic standards, developing best practices for accelerated EKG deployment, curating a repository of reusable models and resources, building a mechanism for engagement and shared knowledge, and advancing the business cases for EKG adoption.

Enterprise Knowledge Graph Maturity Model

The Enterprise Knowledge Graph Maturity Model (EKG/MM) is the industry-standard definition of the capabilities required for an enterprise knowledge graph. It establishes standard criteria for measuring progress and sets out the practical questions that all involved stakeholders ask to ensure trust, confidence and usage flexibility of data. Each capability area provides a business summary denoting its importance, a definition of the added value from semantic standards and scoring criteria based on five levels of defined maturity.


Enterprise Knowledge Graphs is what the Semantic Web Company (SWC) and Ontotext have been about for a long time, too. Two of the vendors in this space that have been around for the longer time just announced a strategic partnership: Ontotext, a graph database and platform provider, meets SWC, a management and added value layer that sits on top.

SWC and Ontotext CEOs emphasize how their portfolios are complementary, while the press release states that the companies have implemented a seamless integration of the PoolParty Semantic Suite™ v.8 with the GraphDB™ and Ontotext Platform, which offers benefits for many use cases.

#database #artificial intelligence #graph databases #rdf #graph analytics #knowledge graph #graph technology

Abdul  Larson

Abdul Larson

1594478340

How to Explain Graph Neural Network — GNNExplainer

Graph Neural Network(GNN) is a type of neural network that can be directly applied to graph-structured data. My previous post gave a brief introduction on GNN. Readers may be directed to this post for more details.

Many research works have shown GNN’s power for understanding graphs, but the way how and why GNN works still remains a mystery for most people. Unlike CNN, where we can extract activation of each layer to visualize the decisions of the network, in GNN it is hard to get a meaningful explanation of what features the network has learnt. Why does GNN determine a node is class A instead of class B? Why does GNN determine a graph is a chemical or molecule? It seems like GNN sees some useful structural information and determines are made upon these observations. But now the problem is, what observations does GNN see?

What is GNNExplainer?

GNNExplainer is introduced in this paper.

Briefly speaking, it is trying to build a network to learn what a GNN has learnt.

The main principle of GNNExplainer is by reducing redundant information in a graph which does not directly impact the decisions. To explain a graph, we want to know what are the crucial features or structures in the graph that affect the decisions of a neural network. If a feature is important, then the prediction should be altered largely by removing or replacing this feature with something else. On the other hand, if removing or altering a feature does not affect the prediction outcome, the feature is considered not essential and thus should not be included in the explanation for a graph.

How does it work?

The primary objective for GNNExplainer is to generate a minimal graph that explains the decision for a node or a graph. To achieve this goal, the problem can be defined as finding a subgraph in the computation graph, that minimizes the difference in the prediction scores using the whole computation graph and the minimal graph. In the paper, this process is formulated as maximizing the mutual information(MI) between the minimal graph Gs and the computation graph G:

Image for post

Besides, there is a secondary objective: the graph needs to be minimal. Though it was also mentioned in the first objective, we need to have a method to formulate this objective as well. The paper addresses it by adding a loss for the number of edges. Therefore, the loss for GNNExplainer is literally the combination of prediction loss and edge size loss.

#graph #graph-neural-networks #graph-theory #pattern-recognition #machine-learning