Given a weighted graph $G = (V,E)$, the in-degree of a node is defined as
$
k\_{in}(i) = \sum\_{j:j \rightarrow i} A\_{ji}
$
where $A\_{ji}$ is the weight of edge from node $j$ to $i$. My question is if there are $m$ nodes pointing to $i$, what's the terminology for $m$? Is it the number of in-links?



The terminology for a node's number of in-links in weighted directed graph
The quantity you are asking about is usually called the "fan-in" of node $i$. The dual quantity which counts the number of nodes to which $i$ points is called the "fan-out". The terms are standard at least in the circuit design and computer science literature, but I can't seem to find them in graph theory texts at the moment. Searching google for something like *directed graph "fan in"* will reveal many papers that use the term.


