+ The most obvious and straightforward node feature to examine is 'degree', which is usually denoted d(u) for a node u ∈ V and simply counts the number of edges incident to a node. 
+  The degree of a node is an essential statistic to consider, and it is often one of the
most informative features in traditional machine learning models applied to node-level tasks.


Node degree

+ Node degree simply measures how many neighbors a node has, but this is not
necessarily sufficient to measure the importance of a node in a graph.
+ We define a node’s eigenvector centrality e(u) via a recurrence relation in which the node’s centrality is proportional to the average centrality of its neighbors.

Node centrality

+ Measures the proportion of closed triangles in a node’s local neighborhood.
+ The popular local variant of the clustering coefficient is computed as follows [Watts and Strogatz, 1998]:

The clustering coefficient

+ An alternative way of viewing the clustering coefficient—rather than as a measure of local clustering—is that it counts the number of closed triangles within each node’s local neighborhood.
+ Rather than just counting triangles, we could consider more complex structures, such as cycles of a particular length. We could also characterize nodes by counts of how often these different motifs occur in their ego graph.

Closed triangles, ego graphs, and motifs

Includes:
 + Node degree.
 + Node centrality.
 + The clustering coefficient.
 + Closed triangles, ego graphs, and motifs.



Saint Olaf College

Graphical methods abstract the dependencies between entities, text and relations in the form of directed acyclic graphs, and then use inference models to identify the correct relations.

Graphical Methods 

Node-level statistics and features


+ Cross-entropy with negative sampling
+ Max-margin loss

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