A finite automaton (finite set of states, finite input alphabet of, say, k letters) can be represented as a k-regular directed multigraph
with ordered edges: the vertices represent the states and the first, second, ...
Let G be a directed multigraph
on n vertices, whose underlying undirected graph is connected.
In the multigraph
associated to a plain matrix substitution system, e is excluded from the set of vertices.
Shao, "A Multigraph
Representation for Improved Unsupervised / Semi-supervised Learning of Human Actions," Cvpr, 2014.
To represent the TTP, a directed multigraph
called discrete time-space graph (DTSG) is proposed .
Abedzadeh, "A time-dependent vehicle routing problem in multigraph
with FIFO property," Journal of Manufacturing Systems, vol.
A simple graph is an undirected graph in which both parallel edges and loops are disallowed while multigraph
otherwise allows them.
If we allow an edge between a vertex and itself (loop) or multiple edges between two vertices, we obtain a multigraph
. An undirected graph without loops or multiple edges is known as a simple graph.
Since the network is created as a multigraph
, two countries may establish more than one connection per year.
Smith, "An algebraic multilevel multigraph
algorithm," SIAM Journal on Scientific Computing, vol.
We assume that our optimization model is formulated based on a directed complete multigraph
G(V, E), where the nodes [v.sub.i] [member of] V represent the trips that contain trip number [n.sub.i], departure station [s.sup.d.sub.i], arrival station [s.sup.a.sub.i], departure time [t.sup.d.sub.i] if, arrival time [s.sup.a.sub.i], distance [S.sub.i], running time [T.sub.i], and train type k--a total of 8 attributes.
A compartmental model (whether in population biology, epidemiology, or pharmacology) is often represented by a diagram such as in Figure 1, which has the form of a directed graph (formally, a directed multigraph
) with labels on arcs.