- [[network formation]], [[python - network packages]], [[network functions]] # Idea When studying networks, we examine how they form, what their structures are, and what [[network functions|functions]] they serve. Networks have nodes and edges. Edges can be directed or undirected. Directed means it's directional (uni or bi-directional). Undirected means no direction. Structure of networks can be quantified by the following: degree, path length, connectedness, clustering coefficient - degree of a node: number of edges connected to a node - degree of a network: average degree of all nodes - $2 \times edges / nodes$ - each edge connects 2 nodes! - proxy for density of connections, [[social capital]], speed of diffusion - neighbors of a node: all other nodes connected by an edge to the node - path length from A to B: minimum number of edges that must be traversed to go from node A to node B - average path length: average path length between all pairs of nodes in a network - flights needed, social distance, likelihood of information spreading - connectedness: how connected a network is - [[Markov processes]], terrorist group capabilities, internet/power failure, information isolation - clustering coefficient: percentage of nodes that have edges between all three nodes - redundancy, robustness, [[social capital]], innovation adoption/triangles Theorem: The average degree of neighbors of nodes will be at least as large as the average degree of the network. - Most poeple's friends are more popular than they are! ![[Pasted image 20210615204504.png|800]] [[Markov processes]] can be represented as networks. ![[Pasted image 20210615205154.png]] # References - https://www.coursera.org/learn/model-thinking/lecture/Er4rf/the-structure-of-networks