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Organizations and their effectiveness-2016/Key concept definitions
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=== Romain === '''Definition:''' a network is a collection of nodes and a collection of ties among these nodes. Types of networks: Several common distinctions are often made when talking about networks. A network can be directed or undirected (tie from $i$ to $j \neq$ tie from $j$ to $i$), and weighted or unweighted. One can also consider static vs. dynamic networks (ties or nodes are created/disappear over time), or multiplex networks (there are several types of ties). When talking about networks, one should always define: (1) what type of network are we talking about, (2) what is a node, (3) what is a tie. Examples: friendship network [type = undirected, unweighted network, node = person, tie = $i$ and $j$ are friends], airport traffic [type = weighted, directed network, node = airport, tie = number of daily flights from airport $i$ to airport $j$] '''(Theoretical) network models:''' Two broad distinctions: (1) network formation vs. process on a network, (2) non-strategic [no game theory] vs. strategic [game theory]. Examples: Non-strategic game of network formation: Barabassi and Albert's model of preferential attachment. Question: Why do networks often exhibit a hub and spoke structure [few nodes with many connections, many nodes with few connections]? Model: start with one node. At each time period, a new node is created and forms 1 tie with some old node selected at random. Old nodes with more connections are selected with higher probability. Strategic game of network formation: Matt Jackson's coauthor's model. Question: how does a population of scholars pick coauthors? Authors choose whether to form ties with other authors. Two authors with a tie are coauthors. Players' utility increases with the number of coauthors, but busy coauthors (ie coauthors with many connections) give less benefits less than non-busy coauthors. Non-strategic process on a network: probabilistic diffusion model. Some disease diffuses on a network. Question: which structures lead to a pandemic (everybody is infected), which do not? On a network, an initial node is infected (the seed). She infects her neighbors with some probability. At each time period, newly infected nodes infect their neighbors with some probability. Strategic process on a network: Chwe's model of social movements. Question: which network structures lead to a revolution (every node protests)? On a network, each node has a threshold. A node protests if the number of her neighbors who protest is above that threshold.
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