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In the process of gene assembling, the molecular structure of a DNA chain, can be modeled by a signed graph. After that by means of a composition of three reduction rules: gnr, gpr and gdr, that is called reduction strategy, this graph is reduced to a null graph. If the composition of any ordering of rules in a reduction strategy such as S, is applicable on a signed graph G, then we say that S can be applied in parallel to G and the set S is said to be a parallel step for reduction of that graph. Also we define the least number of parallel steps in reduction of a graph, to be the parallel complexity of that graph, and denote it C(G). In this thesis, a collection of particular signed graphs,... 

Nowadays Systems in different fields of research like computer science, biology, social networks, information networks, and economics are modeled as graphs. The graphs which model real world systems have very different topological characteristics than those of classic networks. One of the prominent characteristics of these networks, is that its not practical to describe a general model for their structure and behavior. As a consequence of this complexity in modeling and structure, these networks are called complex networks. One of the most important observations in complex networks is the presence of communities, it means that in such networks one can separate vertices in disjoint sets, such...