Algorithm for the Transportation Network Nodes Aggregation Using Fuzzy Logic

In many situations, the model of the transportation network contains a very large number of nodes, so the algorithms operating on such a model may be too time-consuming. Therefore there is a need to simplify the model by reducing the number of nodes. The simplest approach using the physical neighbourhood of the nodes and then aggregation of nearby nodes may be insufficient, because it does not take into account the different roles played by the nodes subject to the merger. Some of them have local significance and can be aggregated without disturbing the traffic flows across the whole network. For other nodes traffic flows associated with geographically distant nodes can be much larger than the local flows. Nodes of this kind should not be aggregated with their neighbours. This paper presents an algorithm for grouping the transportation network nodes using fuzzy logic, which processes the qualitative characteristics of nodes

Visualization of network structure by the application of hypernodes

AbstractIn the literature several authors describe methods to construct simplified models of networks. These methods are motivated by the need to gain insight into the main properties of medium sized or large networks. The present paper contributes to this research by setting focus on weighted networks, the geographical component of networks and introducing a class of functions to model how the weights propagate from one level of abstraction to the next. Hierarchies of network models can be constructed from reordering of the adjacency matrix of the network; this is how “hypernodes” are derived in the present paper. The hypernode algorithm is explored and it is shown how it can be formulated to handle weighted networks. Weighted networks enable handling the uncertainty or the strength of the components which make up the network. The hypernode algorithm can be run in an iterative manner so that a hierarchy of simplified models of the network can be derived. Some case studies demonstrate the hypernode algorithm. In the first case the algorithm is compared with a similar implementation described in the literature. In the second case an airline dataset is analysed. This study shows that when networks are embedded in the geographical space hypernodes may relate to clusters in the spatial domain. The selection of the visual variables to illustrate the strength of the edges and nodes in a weighted network is discussed