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 [6].
Abedzadeh, "A time-dependent vehicle routing problem in
multigraph with FIFO property," Journal of Manufacturing Systems, vol.
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.
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.