Question

Define and describe the complex network theory including its history.

Answer 1

Large graphs of real life are called complex networks. A Complex Network is a network with non-trivial topological features, with
patterns of connection between their elements that are neither purely regular nor
purely random.A complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in graphs modelling of real systems.Most social, biological, and technological networks display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these features also include reciprocity, triad significance profile and other features.

Network theory is the study of graphs as a representation of either symmetric relationsor, more generally, of asymmetric relationsbetween discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be defined as a graph in which nodes and/or edges have attributes .

Network theory has applications in many disciplines including statistical physics, particle physics, computer science, electrical engineering, biology,economics, finance, operations research, climatology and sociology.

Types of networks:
According to the direction of the links: directed or undirected.
According to the kind of interaction: weighted or unweighted.
According to the differences between nodes: bipartite or not.
According to the evolution of their topology: static or evolving.
with/without dynamics.

Euler's solution of the Seven Bridges of Königsberg problem is considered to be the first true proof in the theory of networks.