Graph

Some basic concepts about graph

Graph A graph $\mathcal G$ has nodes $\mathcal V$ and edges $\mathcal E$, $$ \mathcal G = ( \mathcal …

Local Statistics Node Degree Node Degree Node degree of a node $u$ $$ d_u = \sum_{v\in \mathcal V} …

Some basic concepts about graph and traditional algorithms

The [[Ratio Cut]] Graph Cuts Cut For a subset of nodes $\mathcal A\subset \mathcal V$, the rest of …

Graphs can be used in many problem and there are many possible problems on graphs. We will mention a …

mind the data structure: here comes the graph

Over-smoothing is the problem that the representations on each node of the graph neural networks …

Edge sampling is a technique to deal with weighted edges in large [[graph]] What is Graph Graph A …

What problem is StemGNN solving: intra-series temporal pattern: DFT Each series inter-series …

For a given graph $\mathcal G$, we have an attribute on each node, denoted as $f_v$. All the node …

The Katz index is $$ \mathbf S_{\text{Katz}}[u,v] = \sum_{i=1}^\infty \beta^i \mathbf A^i[u, v], $$ …

The LHN index is a normalized similarity index. From Katz Index to LHN Index [[Katz Index]] Graph …

Random Walk Construct a stochastic transfer matrix $P$ by normalizing the adjacency matrix $\mathbf …

For two graphs, $\mathcal G$ and $\mathcal H$, the two graphs are isomorphism on the following …

The Adamic Adar (AA) index is1 $$ \mathbf S_{\text{AA}}[v_1,v_2] = \sum_{u\in\mathcal N(u) \cap …

The Resource Allocation (RA) index is $$ \mathbf S_{\text{RA}}[v_1,v_2] = \sum_{u\in\mathcal N(u) …

The Salton index is $$ \mathbf S_{\text{Salton}}[u,v] = \frac{ 2\lvert \mathcal N (u) \cap \mathcal …

The Sorensen index is $$ \mathbf S_{\text{Sorensen}}[u,v] = \frac{ 2\lvert \mathcal N (u) \cap …

Betweenness centrality of a node $v$ is measurement of how likely the shortest path between two …