Communities.html (3770B)
1 <?xml version="1.0" encoding="UTF-8"?> 2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3 <html><head><link rel="stylesheet" type="text/css" href="sitewide.css"><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/><meta name="exporter-version" content="Evernote Mac 7.1.1 (456663)"/><meta name="keywords" content="ng"/><meta name="altitude" content="-0.8620138168334961"/><meta name="author" content="Alex Balgavy"/><meta name="created" content="2018-05-26 12:39:15 +0000"/><meta name="latitude" content="52.37359333395369"/><meta name="longitude" content="4.83634531063313"/><meta name="source" content="desktop.mac"/><meta name="updated" content="2018-05-26 12:56:08 +0000"/><title>Communities</title></head><body><div>Sociogram: graph-like representation of social structure</div><div>calculate stats like eccentricity, closeness, betweenness centrality</div><div><br/></div><div>proximity prestige</div><ul><li><div>D is digraph with n vertices</div></li><li><div>influence domain R<sup>-</sup>(v) of v is set of vertices from which v can be reached</div></li><li><div>proximity prestige: (fraction of vertices that can reach v) / (average distance of those vertices to v)</div></li></ul><div><br/></div><div>ranked prestige</div><ul><li><div>A is adjacency matrix for digraph</div></li><li><div>A[v,u] means how much v is appreciated by u</div></li></ul><div><br/></div><div style="margin-left: 40px;"><span style="font-size: 20px;" 4 /><img src="Communities.resources/55DEA60A-1653-4137-BADC-C27B9B01534D.png" height="47" width="280"/></div><div><br/></div><div style="margin-left: 40px;"><span style="font-size: 20px;" 5 /><img src="Communities.resources/6CB89EC0-D6C1-42F3-8261-997054B34AE4.png" height="47" width="286"/></div><div><br/></div><div style="margin-left: 40px;"><span style="font-size: 20px;" 6 /><img src="Communities.resources/B313FC5C-6F11-48DC-8B06-C9C398F50428.png" height="43" width="148"/></div><div><br/></div><div style="margin-left: 40px;">example:</div><div style="margin-left: 40px;"><img src="Communities.resources/screenshot_1.png" height="101" width="606"/></div><div><br/></div><div>structural balance</div><ul><li><div>a signed graph (edges labelled +/-) is balanced if all its cycles are positive (product of edge labels is positive)</div></li><li><div>if the graph has no cycles, it is balanced</div></li><li><div>signed graph is balanced iff its vertices can be partitioned into two disjoint subsets such that:</div></li><ul><li><div>each negative edge joins the subsets, and </div></li><li><div>each positive edge joins vertices in the same subset</div></li></ul></ul><div><br/></div><div>affiliation networks</div><ul><li><div>people are tied together through membership relations</div></li><li><div>social structures consist of actors and events</div></li><li><div>naturally bipartite, with two sets (V<sub>a</sub> actors, V<sub>e</sub> events)</div></li><li><div>represented with an actor-event matrix:</div></li></ul><div><br/></div><div style="margin-left: 40px;"><img src="Communities.resources/screenshot.png" height="184" width="582"/></div><div style=""><br/></div><ul><li><div style="">number of events in which a and b participated</div></li></ul><div><br/></div><div style="margin-left: 40px;"><span style="font-size: 20px;" 7 /><img src="Communities.resources/F7861E91-61F2-490E-BD0F-91FEE94A9DE1.png" height="46" width="299"/></div><ul><li><div style="">number of actors participating in events e and f</div></li></ul><div><br/></div><div style="margin-left: 40px;"><span style="font-size: 20px;" 8 /><img src="Communities.resources/4688D813-3907-4209-AE32-6002A873DF1E.png" height="46" width="307"/></div><div><br/></div></body></html>