A node’s ego graph is its local neighborhood viewed as a subgraph. The clustering coefficient summarizes closed triangles in this neighborhood, while motif counts characterize it more broadly by recording how often structures such as triangles or cycles of a specified length occur.

Saint Olaf College

Google

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



Node-level statistics and features


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

Clustering Coefficient

The degree of a node $$u \in V$$, denoted $$d(u)$$, is the most straightforward node-level statistic: it simply counts the number of edges incident to that node. Despite its simplicity, node degree is often one of the most informative features used 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.

Learn Before

Related