Collaborative tagging systems---systems where many casual users annotate objects with free-form strings (tags) of their choosing---have recently emerged as a powerful way to label and organize large collections of data. During our recent investigation into these types of systems, we discovered a simple but remarkably effective algorithm for converting a large corpus of tags annotating objects in a tagging system into a navigable hierarchical taxonomy of tags. We first discuss the algorithm and then present a preliminary model to explain why it is so effective in these types of systems.

http://ilpubs.stanford.edu:8090/775/1/2006-10.pdf

Collaborative Creation of Communal Hierarchical Taxonomies in Social Tagging Systems

Centrality indices are an essential concept in network analysis. For those based on shortest-path distances the computation is at least quadratic in the number of nodes, since it usually involves solving the single-source shortest-paths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.

/pdf/centrality-estimation-in-large-networks-5d6jpuly7e.pdf

Centrality Estimation in Large Networks

We consider variations of two well-known centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the current-flow variant of closeness centrality is identical with another known measure, information centrality, and give improved algorithms for computing both measures exactly. Since running times and space requirements are prohibitive for large networks, we also present a randomized approximation scheme for current-flow betweenness.

/pdf/centrality-measures-based-on-current-flow-5dvzv08330.pdf

Centrality measures based on current flow

Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n2 log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are also the worstcase time bounds for computing the betweenness score of a single vertex. In this paper, we present a novel approximation algorithm for computing betweenness centrality of a given vertex, for both weighted and unweighted graphs. Our approximation algorithm is based on an adaptive sampling technique that significantly reduces the number of single-source shortest path computations for vertices with high centrality. We conduct an extensive experimental study on real-world graph instances, and observe that our random sampling algorithm gives very good betweenness approximations for biological networks, road networks and web crawls.

http://www.cse.psu.edu/~kxm85/papers/ApproxBC-WAW07.pdf

Approximating betweenness centrality

Closeness centrality is an important concept in social network analysis. In a graph representing a social network, closeness centrality measures how close a vertex is to all other vertices in the graph. In this paper, we combine existing methods on calculating exact values and approximate values of closeness centrality and present new algorithms to rank the top-kvertices with the highest closeness centrality. We show that under certain conditions, our algorithm is more efficient than the algorithm that calculates the closeness-centralities of all vertices.

/pdf/ranking-of-closeness-centrality-for-large-scale-social-2yiqjt0290.pdf

Ranking of Closeness Centrality for Large-Scale Social Networks

Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1+epsilon) factor in near-linear time.

Fast Approximation of Centrality

Power law distribution seems to be an important characteristic of web graphs Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs Researchers have conjectured that preferential connectivity and incremental growth are both required for the power law distribution In this paper, we propose a different web graph model with power law distribution that does not require incremental growth We also provide a comparison of our model with several others in their ability to predict web graph clustering behavior

A steady state model for graph power laws

Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1 + ∈) factor in near-linear time.

/pdf/fast-approximation-of-centrality-11200jn86o.pdf

Fast approximation of centrality

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have conjectured that preferential connectivity and incremental growth are both required for the power law distribution. In this paper, we propose a different web graph model with power law distribution that does not require incremental growth. We also provide a comparison of our model with several others in their ability to predict web graph clustering behavior.

/pdf/a-steady-state-model-for-graph-power-laws-4yea931gcb.pdf

Joseph Wang

Papers

Fast Approximation of Centrality

A steady state model for graph power laws

Fast approximation of centrality

A steady state model for graph power laws

Fast Approximation of Centrality