Fig. 2
From: Estimation of traffic flow changes using networks in networks approaches
NiN dynamics for traffic flow change example. a Visualisation of the underlying infrastructure network. b Incidence graph of the NiN model with the associated adjacency matrices of the hypervertices. (1) Change of the path topology. (2) Update of the edges and weights. (3) Random walker to determine path changes. (4) Random walker to determine cascading effects. (5) Modification and assessment of not directly influenced paths. (i), (ii), and (iii) show the network representations of the adjacency matrices, i.e. the Markov chains. (i) Travellers which original use path \(v_{1}^{\gamma }\) have to diffuse to \(v_{2}^{\gamma }\) or \(v_{3}^{\gamma }\), also a change between \(v_{2}^{\gamma }\) and \(v_{3}^{\gamma }\) is possible. The strength of the cascading effect is determined in (ii), which influences the traffic flow redistribution in (iii)