On local primitiveness of graphs and nonnegative matrices

Cryptographic generators constructed of control and generating blocks are investigated. Essential dependence of block elements on all signs of generator initial state is the useful property of such generators. The notion of a local primitiveness for a nonnegative matrix or graph is introduced to study such dependences. The conditions for matrix local primitiveness are obtained. A relation between the local primitiveness characteristics of matrices (graphs) of particular classes and parameters of generators is established.