PPT-Degree and Eigenvector Centrality

The Centralities Degree Centrality 2 The Centralities Quality what makes a node important central Mathematical Description Appropriate Usage Identification Lots of onehop. Centrality measures. Centrality measures. Centrality is related to the potential importance of a node. Some. nodes have greater “influence” over others compared to the rest,. or are more easily accessible to other, or act as a go-between in. 7. Centrality (. cont. ). Slides modified from . Lada. . Adamic. and . Dragomir. . Radev. Outline. Degree centrality. Centralization . Betweenness. centrality. Closeness centrality. Eigenvector centrality. Hexmoor. Department of Computer Science. Southern Illinois University Carbondale. Network Theory:. Computational Phenomena and Processes. Social Network Analysis . Degree, . Indegree. , . Outdegree. Centrality. Betweenness. and Graph partitioning. Chapter 3, from D. Easley and J. Kleinberg book. Section 10.2.4, from A. . Rajaraman. , J. Ullman, J. . Leskovec. Centrality Measures. Not all nodes are equally important. : Graph-based Centrality as Salience in Text Summarization. Gunes. . Erkan. Department of EECS. University of Michigan. Dragomir. R. . Radev. School of Information & Department of EECS. University of Michigan. Devavrat Shah. LIDS+CSAIL+EECS+ORC. Massachusetts Institute of Technology. Network centrality. It’s a graph score function . Given graph G=(V, E). Assigns “scores” to nodes in the graph. That is, . TJTSD66: Advanced Topics in Social Media. Dr. WANG, Shuaiqiang @ CS & IS, JYU. Email: . shuaiqiang.wang@jyu.fi. Homepage: . http://users.jyu.fi/~swang/. (Social . Media . Mining). Klout. Why Do We Need Measures?. Eigenvector Centrality •Node has high score if connected to many –Computed as:•Indicator of popularity, “in the know”•Like degree, is index of exposure, risk•Tends t (Gephi and Python). By: Ralucca Gera, NPS. Excellence Through Knowledge. Python with Networkx. Excellence Through Knowledge. Python code . Use . Metrics.py . from dropbox or . my . website. 3. NetworkX Reference. Excellence Through Knowledge. A periodic table of centralities. 2. An interactive periodic table of centralities: . http://. schochastics.net/sna/periodic.html. Different types of centralities:. 3. Source: Discovering Sets of Key Players in Social Networks – Daniel Ortiz-Arroyo – Springer 2010/. Quality:. what makes a node important (central). Mathematical. Description. Appropriate Usage. Identification. Lots of one-hop. connections from . The number of vertices that . influences directly. Steven Fitzpatrick. Martha Winger-Bearskin. ‘. Intuitive’ Problems . Hamiltonian Problems. Possible Implementations . Traffic Analysis. Spread of Disease. Political Campaigns. Market Analysis. Link Analysis. Gephi). Python code . Use . Metrics.py . from . the workshop’s website. 2. NetworkX Reference. PDF reference for NetworkX. Github interactive version. 3. Finding centralities. The part of the. code that finds . Algorithmic and Economic Aspects of Networks Nicole Immorlica Syllabus Jan. 8 th (today): Graph theory, network structure Jan. 15 th : Random graphs, probabilistic network formation Jan. 20 th : Epidemics