This necessitates formulate discrete operators on graphs which are analogous to differential operators in calculus, such as graph Laplacians (or discrete Laplace operators) as discrete versions of the Laplacian, and use these operators to formulate differential equations, difference equations, or variational models on graphs which can be interpreted as discrete versions of partial differential equations or continuum variational models. In applications, finite weighted graphs represent a finite number of entity by the graph's vertices, any pairwise relationships between these entity by graph edges, and the meaning of a relationship by an edge weight function.

COMING SOON!

```
package org.gs.graph
import scala.collection.mutable.ListBuffer
/** Common code for edge weighted graphs
*
* @constructor called by subclass with number of vertices
* @tparam A BaseEdge, superclass of Edge or DirectedEdge
* @param numV vertices in EdgeWeightedGraph or EdgeWeightedDigraph
* @see [[https://algs4.cs.princeton.edu/43mst/EdgeWeightedGraph.java.html]]
* @author Scala translation by Gary Struthers from Java by Robert Sedgewick and Kevin Wayne.
*/
abstract class BaseEdgeWeightedGraph[A <: BaseEdge](val numV: Int) {
require(numV >= 0, s"Number of vertices, v:$numV must be nonnegative")
protected[gs] var e = 0
protected[gs] val _adj = Array.fill[List[A]](numV)(List[A]())
protected def buildADJ[U <: BaseEdgeWeightedGraph[A]](g: U): Unit = {
e = g.e
for {
v <- 0 until g.numV
e <- g.adj(v)
} e :: _adj(v)
}
protected def rangeGuard(x: Int): Boolean = x match {
case x if 0 until numV contains x => true
case _ => false
}
/** returns edges incident on v */
def adj(v: Int): List[A] = {
require(rangeGuard(v), s"verticies v:$v not in 0..$numV ")
_adj(v)
}
/** abstract edges in graph */
def edges(): List[A]
override def toString(): String = {
val lf = sys.props("line.separator")
val sb = new StringBuilder()
sb append (s"$numV $e $lf")
def addLines(v: Int) {
sb append (s"$v : ")
_adj(v) foreach (ed => sb append (s"$ed "))
sb append (lf)
}
for(v <- 0 until numV) addLines(v)
sb.toString
}
}
```