Structural and dynamical analysis of complex networks

We encounter in real world large networks as diverse as neural networks, power grid, financial networks, friendship networks, Internet, WWW. These networks are commonly characterized by a large number of highly interconnected dynamical entities. They are so complex that they may give birth to many dynamic phenomena. Understanding at the same time the topological and dynamical aspect of complex networks is an important challenge. In this paper, we review on the fundamental elements of complex networks study. We include definitions, measurements, models used to analyse topology and dynamics of these systems. Moreover, we discuss some questions related to mobility and dynamic community detection in complex systems. Introduction For a long time, networks have been studied with great importance in many domains that are scientific or not. The study of networks has mostly developed in research fields such as social sciences, physics, computer sciences and molecular biology. A network is an abstract representation of entities or elements as regards a domain with nodes (or points) and their relationships (or interactions) with links called edges. Known in the mathematical field as graph, a network can represent for instance the rumour spreading in a social network such as the nodes whose individuals and links represent their diverse relationships, or Internet whose nodes are devices (computers, routers ...) and links are the cables or the air. The late 1990s witnessed a boom of research activities around the study of networks said 'complex' (i.e. networks whose structure is irregular, complex and dynamically evolving in time [12]) which are, generally, the result of decentralized and planed evolution. Indeed, the study of complex networks has known dramatic advances sustained by the recent appearance of large databases that allow studying systematically the topology of various real networks and the increased computing power allows us to explore networks containing millions of nodes. Some deficiencies observed in the complex networks modelling based on graph theory has led researchers to introduce new definitions and metrics, which help us to mimic their structure and their dynamic evolution. In spite of many models proposed, the problem concerning the dynamic evolution in a network is a subject which interests researchers in complex networks area. For this reason, we study, analyse and try to understand the two aspects that are the structure and the dynamic evolution of complex networks. This report is divided into four sections organized as follows: First, in section 1, we give a description of a complex network in order to explain what is the origin of this science and where do we find it. In section 2, we describe in detail the structure of complex networks by reviewing the different definitions, notations and metrics, and the different benchmark models of networks such as random graphs, small world and the scale free. After, in section 3, we explain how we understand dynamics in a complex network and we propose some approaches used to model this dynamics. Finally, we exhibit in section 4 some problems and perspectives related such as mobility and community detection in dynamic networks. 2nd Information Technology and Mechatronics Engineering Conference (ITOEC 2016) © 2016. The authors Published by Atlantis Press 126