en>Mogism: /* Example of pole splitting */Cleanup/Typo fixing, typos fixed: , → , using AWB

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Example of pole splitting: Cleanup/Typo fixing, typos fixed: , → , using AWB

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	I'~~m Tatum but my husband doesn~~'~~t like it~~ at ~~practically all~~. ~~In her professional life~~ is ~~actually~~ a ~~manager but soon her husband~~ and ~~her will start their own business~~. ~~Years ago she moved to Alaska~~. It'~~s actually common thing~~ but ~~what she likes doing~~ is ~~bee keeping but she's been taking on new things lately~~. ~~I've been repairing my website for time now~~. ~~Take~~ a ~~visit here~~: http://www.~~apymeelhierro~~.~~org~~/~~new~~/[~~http~~://~~thesaurus~~.~~com~~/~~browse~~/~~outlet-ugg~~.~~html outlet-ugg~~.~~html~~]<br><br>~~Check out my blog;~~ [~~http:~~//~~www~~.~~apymeelhierro~~.~~org~~/new/~~outlet-ugg.html Outlet Ugg~~]		'''Triadic closure''' is a concept in [[social network]] theory, first suggested by [[Germany\|German]] [[sociology\|sociologist]] [[Georg Simmel]] in the early 1900s.<ref>[http://www.nytimes.com/2007/12/17/style/17facebook.html?pagewanted=print Georg Simmel], originator of the concept: "Facebook" article at [[the New York Times]] website. Retrieved on December 21, 2007.</ref> Triadic closure is the property among three nodes A, B, and C, such that if a strong tie exists between A-B and A-C, there is a weak or strong tie between B-C.<ref>[http://serendip.brynmawr.edu/complexity/course/emergence06/bookreviews/kmaffei.html Working concept] of triadic closure: book review of [[Duncan Watts]]' "[[Six Degrees: The Science of a Connected Age]]" at the ''Serendip'' ([[Bryn Mawr College]]) website. Retrieved on December 21, 2007.</ref> This property is too extreme to hold true across very large, complex networks, but it is a useful simplification of reality that can be used to understand and predict networks.<ref name=Easley>Easley, D, & Kleinberg, J. (2010). Networks, crowds, and markets: reasoning about a highly connected world. Cornell, NY: Cambridge Univ Pr.</ref>

			==History==
			Triadic closure was made popular by [[Mark Granovetter]] in his 1973 article ''The Strength of Weak Ties''.<ref>Granovetter, M. (1973). "[http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granstrengthweakties.pdf The Strength of Weak Ties]", American Journal of Sociology, Vol. 78, Issue 6, May 1360-80.</ref> There he synthesized the theory of [[cognitive balance]] first introduced by [[Fritz Heider]] in 1946 with a Simmelian understanding of social networks. In general terms, cognitive balance refers to the propensity of two individuals to want to feel the same way about an object. If the triad of three individuals is not closed, then the person connected to both of the individuals will want to close this triad in order to achieve closure in the relationship network.

			==Measurements==
			{{Unreferenced section\|date=September 2009}}
			The two most common measures of triadic closure for a graph are (in no particular order) the [[clustering coefficient]] and transitivity for that graph.

			===Clustering coefficient===
			One measure for the presence of triadic closure is [[clustering coefficient]], as follows:

			Let <math>G = (V,E)</math> be an undirected simple graph (i.e., a graph having no self-loops or multiple edges) with V the set of vertices and E the set of edges. Also, let <math>N = \|V\|</math> and <math>M = \|E\|</math> denote the number of vertices and edges in G, respectively, and let <math>d_i</math> be the [[degree (graph theory)\|degree]] of vertex i.

			Then we can define a triangle among the triple of vertices <math>i</math>, <math>j</math>, and <math>k</math> to be a set with the following three edges: {(i,j), (j,k), (i,k)}. Then we can define the number of triangles that vertex <math>i</math> is involved in as <math>\delta (i)</math> and, as each triangle is counted three times, we can express the number of triangles in G as <math>\delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i)</math>. Assuming that triadic closure holds, only two strong edges are required for a triple to form and the number of triples of vertex i is <math>\tau (i) = \binom{d_i}{2}</math>, assuming <math>d_i \ge 2</math>. Thus we can express <math>\tau (G) = \frac{1}{3} \sum_{i\in V} \ \tau (i)</math>.

			Now, for a vertex <math>i</math> with <math>d_i \ge 2</math>, the [[clustering coefficient]] <math>c(i)</math> of vertex <math>i</math> is the fraction of triples for vertex <math>i</math> that are closed, and can be measured as <math>\frac{\delta (i)}{\tau (i)}</math>. Thus, the [[clustering coefficient]] <math>C(G)</math> of graph <math>G</math> is given by <math>C(G) = \frac {1}{N_2} \sum_{i \in V, d_i \ge 2} c(i)</math>, where <math>N_2</math> is the number of nodes with degree at least 2.

			===Transitivity===
			Another measure for the presence of triadic closure is transitivity, defined as <math>T(G) = \frac{3\delta (G)}{\tau (G)}</math>.

			==Causes and effects==
			In a trust network, triadic closure is likely to develop due to the transitive property. If a node A trusts node B, and node B trusts node C, node A will have the basis to trust node C. In a social network, strong triadic closure occurs because there is increased opportunity for nodes A and C with common neighbor B to meet and therefore create at least weak ties. Node B also has the incentive to bring A and C together to decrease the latent stress in two separate relationships.<ref name=Easley/>

			Networks that stay true to this principle become highly interconnected and have very high clustering coefficients. However, networks that do not follow this principle turn out to be poorly connected and may suffer from instability once negative relations are included.

			Triadic closure is a good model for how networks will evolve over time. While simple graph theory tends to analyze networks at one point in time, applying the triadic closure principle can predict the development of ties within a network and show the progression of connectivity.<ref name=Easley/>

			In social networks, triadic closure facilitates cooperative behavior, but when new connections are made via
			referrals from existing connections the average global fraction of cooperators is less than when individuals choose new connections randomly from the population at large. Two possible effects for this are by the structural and informational construction. The structural construction arises from the propensity toward high clusterability. The informational construction comes from the assumption that an individual knows something about a friend's friend, as opposed to a random stranger.

			==Strong Triadic Closure Property and local bridges==
			Strong Triadic Closure Property is that if a node has strong ties to two neighbors, then these neighbors must have at least a weak tie between them. A [[local bridge]] occurs, on the other hand, when a node is acting as a gatekeeper between two neighboring nodes who are not otherwise connected. In a network that follows the Strong Triadic Closure Property, one of the ties between nodes involved in a local bridge needs to be a weak tie.

			===Proof by contradiction===

			Let node B be a local bridge between nodes A and C such that there is no weak tie between the nodes involved. Therefore B has a strong tie to both A and C. By the definition of Strong Triadic Closure, a weak tie would develop between nodes A and C. However, this contradicts the fact that B is a local gatekeeper. Thus at least one of the nodes involved in a local bridge needs to be a weak tie to prevent triadic closure from occurring.<ref name=Easley/>

			==References==
			{{Reflist}}

			{{Social networking}}

			{{DEFAULTSORT:Triadic Closure}}
			[[Category:Social systems]]
			[[Category:Sociological terminology]]

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I'm Tatum but my husband doesn't like it at practically all. In her professional life is actually a manager but soon her husband and her will start their own business. Years ago she moved to Alaska. It's actually common thing but what she likes doing is bee keeping but she's been taking on new things lately. I've been repairing my website for time now. Take a visit here: http://www.apymeelhierro.org/new/[http://thesaurus.com/browse/outlet-ugg.html outlet-ugg.html]<br><br>Check out my blog; [http://www.apymeelhierro.org/new/outlet-ugg.html Outlet Ugg]

Pole splitting - Revision history

en>Mogism: /* Example of pole splitting */Cleanup/Typo fixing, typos fixed: , → , using AWB

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