### Graph Reduction Algorithm without Loss of Information

#### Abstract

Algorithms related to graph theory have been studied widely. Several studies deal with the reduction of temporal complexity of these algorithms. The techniques used in this sense are generally based on reducing the graph or the search space of solution. These approaches remove redundant information for a specific kind of problem. The process of reducing a graph is based on obtaining smaller graphs (with fewer vertices) with major or relevant characteristics of the original graph. Algorithms that make use of the graph reduction approach (or reduction of solution search space) for the shortest path search do not guarantee obtaining an optimal path in all cases. The same applies to other types of problems such as graph reduction in workflow networks, computer networks, etc. In this paper we propose a graph reduction algorithm without loss of information. Our method is characterized by a flexible way to specify in what manner in it desirable to reduce a given graph. Therefore, our proposal can be used in solving various types of problems and obtaining optimal responses in less time.

#### Keywords

Graph reduction; graph rewriting; shortest path search.