Abstract
The tendency of humans to connect with one another is a deep-rooted social need that precedes the advent of the Web and Internet technologies. In the past, social interactions were achieved through face-to-face contact, postal mail, and telecommunication technologies. The last of these is also relatively recent when compared with the history of mankind. However, the popularization of the Web and Internet technologies has opened up entirely new avenues for enabling the seamless interaction of geographically distributed participants. This extraordinary potential of the Web was observed during its infancy by its visionary founders. However, it required a decade before the true social potential of the Web could be realized. Even today, Web-based social applications continue to evolve and create an ever-increasing amount of data. This data is a treasure trove of information about user preferences, their connections, and their influences on others. Therefore, it is natural to leverage this data for analytical insights.
“I hope we will use the Net to cross barriers and connect cultures.”—Tim Berners-Lee
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Notes
- 1.
Without loss of generality, it can be assumed that the graph contains an even number of nodes, by adding a single dummy node.
- 2.
Moving a node from one partition to the other will frequently cause violations unless some flexibility is allowed in the balancing ratio. In practice, a slight relaxation (or small range) of required balancing ratios may be used to ensure feasible solutions.
- 3.
The normalized values, such as those in Eq. 19.13, may be obtained by dividing the unnormalized values by \(n\cdot (n-1)\) for a network with \(n\) nodes. The constant of proportionality is irrelevant because the Girvan–Newman algorithm requires only the identification of the edge with the largest betweenness.
- 4.
In practice, the unit eigenvectors of \(\Lambda ^{-1}L\) can be directly computed, and therefore an explicit post-processing step is not required.
- 5.
- 6.
In other words, the underlying Markov chain is not strongly connected, and therefore not ergodic. See the description of the PageRank algorithm in Chap. 18.
- 7.
In this case, the regularizer ensures that no single entry in \(\overline {Z_c}\) for unlabeled nodes is excessively large.
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© 2015 Springer International Publishing Switzerland
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Aggarwal, C. (2015). Social Network Analysis. In: Data Mining. Springer, Cham. https://doi.org/10.1007/978-3-319-14142-8_19
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DOI: https://doi.org/10.1007/978-3-319-14142-8_19
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