 - If edges are undirected then the adjacency matrix is a symmetric matrix.
 - If edges are directed then the adjacency matrix need not be a symmetric matrix.
 - Some graphs have weighted edges, so the entries in the adjacency matrix are real values rather than 0 or 1.


San Jose State University

A graph $\mathcal{G} = ( \mathcal{V},\mathcal{E})$ is a set of nodes and edges.
An edge going from node $u \in \mathcal{V}$ to node $v \in \mathcal{V}$  is denoted as $(u,v) \in \mathcal{E}$


Mathematical Representation of Graph Data

Hamilton, W.L. Graph Representation Learning. *Synthesis Lectures on Artificial Intelligence and Machine Learning*. 2020, 14(3), 1–159. https://doi.org/10.2200/S01045ED1V01Y202009AIM046

Graph Representation Learning by William Hamilton

Graphs can be represented using the adjacency matrix $ A \in {\rm I\!R} ^{|\mathcal{V}| \times  |\mathcal{V}| }$

Each node in the graph has a row and a column in the adjacency matrix.

The presence of edges is  represented as an entry in the matrix as  $ A[u,v] = 1 $ if $ (u,v) \in \mathcal{E}$ and $ A[u,v] = 0 $ otherwise


Learn Before

Related