In today's lecture we learned about the Mathematics of Networks. Networks are composed of points (vertices, nodes, sites, etc), lines (edges, links, bonds, etc), and a Domain (math, coputer science, physics, etc). We learned about the relations of nodes to each other in directed and undirected networks and how the edges can have different meaning such as weight, ranking, type, etc. Edges can also be negative and it can be confusing deciding what they mean. Talked about Adjacency matrices and how to create them from a directed or undirected graph, and went over adjacency lists, and matrix notation. Talked about finding the degree of nodes and doing matrix multiplication on Bipartite networks and how to collapse a two-mode network to a one mode-network.
Networks are equivalent to graphs and are graphed in many different ways depending on the type on network such as Planar graphs, tree graphs, and Hyper graphs.
Planar graphs are graphs that can be drawn without any of the edges crossing.
Tree graphs are undirected and contain no cycles.
Hyper graphs are graphs that join more than two nodes at a time (hyperEdge).
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