Sep Kamvar’s monograph presents work from his 2004 thesis on how numerical algorithms are a critical component in search systems. Kamvar focuses on the new information networks arising in the late 1990s and early 2000s. When originally published, these results were groundbreaking and resulted in an NSF press release and even a Slashdot listing. 2 The book is divided into two parts, one for each...

[Background]Discovering key nodes plays a significant role in Social Network Analysis(SNA). Effective and accurate mining of key nodes promotes more successful applications in fields like advertisement and recommendation. [Methods] With focus on the temporal and categorical property of users’ actions when did they re-tweet or reply a message, as well as their social intimacy measured by structu...

Google’s success derives in large part from its PageRank algorithm, which ranks the importance of web pages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course. Instructors may assign this article as a project to more advanced students or spend one or two lectures presenting the material with assi...

We show that whenever there is a sharp drop in the numerical rank defined by a personalized PageRank vector, the location of the drop reveals a cut with small conductance. We then show that for any cut in the graph, and for many starting vertices within that cut, an approximate personalized PageRank vector will have a sharp drop sufficient to produce a cut with conductance nearly as small as th...

With the evolution of IT technologies, large-scale graph data have lately become a growing interest. As a result, there are a lot of research results in large-scale graph analysis on Hadoop. The graph analysis based on Hadoop provides parallel programming models with data partitioning and contains iterative phases of MapReduce jobs. Therefore, the effectiveness of data partitioning depends on h...

The ranking of sports teams is of significant importance to those who are involved with or interested in the various professional and amateur leagues that exist around the world. We present a ranking algorithm that is simple to implement in SAS code and which gives results that are consistent with some of the best and most well-known computer methods for ranking sports teams. Whether you are tr...

A local partitioning algorithm finds a set with small conductance near a specified seed vertex. In this paper, we present a generalization of a local partitioning algorithm for undirected graphs to strongly connected directed graphs. In particular, we prove that by computing a personalized PageRank vector in a directed graph, starting from a single seed vertex within a set S that has conductanc...

In this work we introduce and study a nonlocal version of the PageRank. our approach, random walker explores graph using longer excursions than just moving between neighboring nodes. As result, corresponding ranking nodes, which takes into account \textit{long-range interaction} them, does not exhibit concentration phenomena typical spectral rankings take local interactions. We show that predic...

When computing on massive graphs, it is not tractable to iterate over the full graph. Local graph methods aim to analyze properties in a neighborhood of a seed vertex. Graph partitioning is an example of a problem that has a local analog. It attempts to find a sparse cut of a specific volume near a seed vertex. Previous work attempts to approximate the optimal partition through standard, PageRa...

The PageRank algorithm is used by the popular Google search engine to rate website reputation. It is one of the key ingredients that affects placement in search results coveted by webmasters. I prove that attempts to manipulate a site’s PageRank by creating “link farms” are futile, and that PageRanks can only be increased by either recommendations from reputable websites or by buying domain nam...