Networks: Definitions

This lecture introduces the concept of networks as systems of interconnected elements with low local complexity and high global complexity, represented as mathematical objects capturing complex structures with simple elements. It covers the definition of graphs with vertices and edges, including an example. The lecture also explains subgraphs as subsets of vertices and edges within a larger graph, and directed graphs with nodes and arcs, emphasizing injective functions and unique arcs. Additionally, it defines indegree as the number of arcs entering a node.