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In [[graph theory]] and [[social network analysis]], '''alpha centrality''' is a measure of [[centrality]] of nodes within a [[Graph (mathematics)|graph]]. It is an adaptation of [[eigenvector centrality]] with the addition that nodes are imbued with importance from external sources.
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==Definition==
Given a graph with [[adjacency matrix]] <math>A_{i,j}</math> the alpha centrality is defined as follows:
 
:<math> x = (I-\alpha A^T)^{-1}e \, </math>
 
where <math>e_j</math> is the external importance given to node <math>j</math>, and <math>\alpha</math> is a parameter.<ref>{{cite journal  | author = P. Bonacich, P. Lloyd  | title = Eigenvector-like measures of centrality for asymmetric relations  | url = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VD1-43G39CH-2&_user=10&_coverDate=07%2F31%2F2001&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=c7c10c464e20246d9d67970415887487&searchtype=a  | doi=10.1016/S0378-8733(01)00038-7}}</ref>
 
==Motivation==
 
To understand alpha centrality one must first understand Eigenvector Centrality. An intuitive process to compute eigenvector centrality is to give every node a starting random positive amount of influence. Each node then splits its influence evenly and divides it amongst its outward neighbors, receiving from its inward neighbors in kind. This process repeats until everyone is giving out as much as they're taking in and the system has reached steady state. The amount of influence they have at this steady state is their eigenvector centrality. Computationally this process is called the [[power method]]. We know that this process has converged when the vector of influence changes only by a constant as follows.
:<math>x_i = \frac{1}{\lambda} A^T_{i,j}x_j</math>
Where <math>x_i</math> is the amount of influence that node <math>i</math> carries, <math>A_{i,j}</math> is the adjacency matrix and <math>\lambda</math> happens to be the principal eigenvalue (although this is not terribly important here).
 
Alpha centrality enhances this process by allowing nodes to have external sources of influence. The amount of influence that node <math>i</math> receives at every round is encoded in <math>e_i</math>. The process described above should now stop when
 
:<math> x_i = \alpha A^T_{i,j}x_j + e_i \, </math>
 
Where <math>\alpha</math> is a constant that trades off the importance of external influence against the importance of connection. When <math>\alpha=0</math> only the external influence matters. When <math>\alpha</math> is very large then only the connectivity matters, i.e. we reduce to the eigenvector centrality case.
 
Rather than perform the iteration described above we can solve this system for <math>x</math>, obtaining the following equation:
 
:<math> x = (I-\alpha A^T)^{-1}e \, </math>
 
==Applications==
Alpha centrality is implemented in igraph library for network analysis and visualization.<ref>http://igraph.sourceforge.net/doc/R/alpha.centrality.html</ref>
 
==See also==
* [[Eigenvector centrality]]
 
==Notes and references==
{{Reflist}}
 
[[Category:Algebraic graph theory]]
[[Category:Network analysis]]
[[Category:Social networks]]
 
[[es:Centralidad]]
[[ar:مركزية ألفا]]

Latest revision as of 18:37, 7 January 2015

Email marketing is a marketing method that uses emails to promote to customers. To some, this can sound a bit difficult, but it really isn't. Using email marketing to reach your customer base isn't as hard as you might think, especially if you pay close attention to the tips in the following article.



Develop a consistent format and schedule for your marketing emails. By doing this, your customers will learn when and what to expect. Find a professional template that suits your business and used it every time. Alert your customers to the most relevant information at the beginning of the email.

Try different email formats. Your email should be like a funnel, with the most important items at the top and the least important items at the bottom. Trying out different layouts will help you find what works the best. Once you know which ones will work and which ones won't, keep doing the successful ones! This helps your customers become familiar with your business, so they always know where to go in order to get additional information from you.

Data mine your email list and bucket your audience into various segments based off of any profiling data you have. This will allow you to be more strategic with your messaging and effectively increase your chances of higher open and click through rates. Even if you don't have profiling, look to geo-targeting. Various regions respond differently to different types of messaging.

Don't spam your customer base; get permission to send emails. If your emails are considered spam, you won't be taken seriously. Some may dislike unwanted emails so much, they decide to no longer buy from you or work with you.

Strategically plan when your emails will go out. People do not like getting emails at inconvenient times, especially if it's something that they have to act on quickly. Be considerate by making your offers convenient and easy for people to take advantage of, and you will have more sales than you otherwise would.

Get creative with your email designs to find out what works best. Send out a few emails with content and links that differ in their fonts and text color. Play around with image positioning, including buttons and logos. After you've sent the emails, find out which ones had the best click-thru rates. Stick with those for the time being, but change it up on occasion to see if you can find a method that works even better. More click-thru rates equate to more sales.

When you are setting up an email marketing campaign, it is pertinent to know who your target audience is. The proper research regarding your market niche will help you determine your target audience, and you can then build an effective email marketing campaign. Targeting the right customers is key to your success.

Use feedback, that is both active and passive, to improve your marketing campaigns. Active feedback can be gained by asking your readers for suggestions. Passive feedback is much more subtle and not noticeable to the reader. You can get tools and software that can help you to figure out what links have the most clicks.

Pay attention to the demographics within your subscriber base. See what content and links intrigued a particular segment of your audience, and then follow up with a new email to that subgroup. The boost in your response rate from peeling away the top layer will really surprise you, but in a delightful way.

You should know that an email previewing feature allows users to see the pre-header of your email without opening it. A preheader works by taking the initial line of email text and making it highlighted at the beginning. This is a fabulous way to grab the viewer's attention as this piece of text is normally displayed immediately after the subject line by some email service providers.

Hopefully now that you have read this article, you are a little less intimidated by email marketing. The widely used marketing practice is fairly simple to implement and can be adapted in no time at all. Simply remember all of the tips that you read here and you will be on your way to using emails for marketing.

If you have any kind of concerns pertaining to where and the best ways to use free email address, you could call us at the page.

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