Complex networks are everywhere in nature,in our lives. A complex network is composed of nodes or vertices which are the members of a system. These members(or nodes) are then connected according to a relation among each other(ie. friendship etc.) The nodes are connected to each other if they have the relation. The whole graph is called a complex network. Internet, friendship networks, food network are some examples of complex networks.
Of course a complex network has some characteristics, not every network is complex. If we talk about complex networks, then it should have small-world property and it should be scale-free.
I will be giving the definitions soon, with the exact references.
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