### Multi-relational graphs

## Multi-relational graph

- One where edges have a
*type*

- Two nodes can be connected by multiple edges so long as they have different types.

## Graphs where edges have a type

Multi-relational

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## Heterogeneous graph

One where edges and nodes have a

*type*## Graphs where edges and nodes have a type

Heterogeneous graphs

## What is often the case regarding edge and node types in a heterogeneous graph?

A given edge type only connect nodes of specific types.

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## Multipartite graph

One where edges can only connect nodes that have different types

## Graphs where edges can only connect nodes that have different types

Multipartite graph

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## Multiplex graph

- Multi-relational graph

- Edges are composed into layers

- Intra-layer edges as before

- Plus inter-layer edges connecting the
*same*node

## Multi-relational graph decomposed into layers

Multiplex graph

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### ML on graphs

#### Node classification

## What are we trying to predict with node classification, based on what?

The classes of unlabelled nodes, based on the classes of labelled ones & complete node features.

## Key difference between regular supervised datasets and node-level graph-based datasets

We no longer have the i.i.d. assumption

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## Homophily

The tendency for nodes to share attributes with their neighbours

## The tendency for nodes to share attributes with their neighbours

Homophily

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## Structural equivalence (graphs)

The tendency for nodes with similar local neighborhood structures to have similar labels

## The tendency for nodes with similar local neighborhood structures to have similar labels

Structural equivalence

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## Heterophily

The tendency for nodes to have different attributes to their neighbours

## The tendency for nodes to have different attributes to their neighbours

Heterophily

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## In what way is node-classification like and unlike semi-supervised learning?

**Like:**we have access to the edges (and features?) of the unlabelled nodes

**Unlike:**we don't have the i.i.d. assumption

#### Link prediction

## What are we trying to predict with link prediction, based on what?

Edges between nodes, based on an incomplete set of edges between nodes & complete node features.

#### Community Detection

## What is community detection (at a high-level)?

Infering the latent community structures in a (single) graph

### Graph-level tasks

## What are the data-points for graph classification, regression and clustering

Entire graphs