We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Roberta Comunian tackles head-on some of the dilemmas and challenges which this promising new methodology raise for a researcher in regional studies.

Social Network Analysis

https://kops.uni-konstanz.de/bitstream/handle/123456789/5940/variants.pdf;sequence=1

On variants of shortest-path betweenness centrality and their generic computation ☆

miRNet is an easy-to-use, web-based platform designed to help elucidate microRNA (miRNA) functions by integrating users' data with existing knowledge via network-based visual analytics. Since its first release in 2016, miRNet has been accessed by >20 000 researchers worldwide, with ∼100 users on a daily basis. While version 1.0 was focused primarily on miRNA-target gene interactions, it has become clear that in order to obtain a global view of miRNA functions, it is necessary to bring other important players into the context during analysis. Driven by this concept, in miRNet version 2.0, we have (i) added support for transcription factors (TFs) and single nucleotide polymorphisms (SNPs) that affect miRNAs, miRNA-binding sites or target genes, whilst also greatly increased (>5-fold) the underlying knowledgebases of miRNAs, ncRNAs and disease associations; (ii) implemented new functions to allow creation and visual exploration of multipartite networks, with enhanced support for in situ functional analysis and (iii) revamped the web interface, optimized the workflow, and introduced microservices and web application programming interface (API) to sustain high-performance, real-time data analysis. The underlying R package is also released in tandem with version 2.0 to allow more flexible data analysis for R programmers. The miRNet 2.0 website is freely available at https://www.mirnet.ca.

miRNet 2.0: network-based visual analytics for miRNA functional analysis and systems biology.

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

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 present a novel sampling-based approximation technique for classical multidimensional scaling that yields an extremely fast layout algorithm suitable even for very large graphs. It produces layouts that compare favorably with other methods for drawing large graphs, and it is among the fastest methods available. In addition, our approach allows for progressive computation, i.e. a rough approximation of the layout can be produced even faster, and then be refined until satisfaction.

/pdf/eigensolver-methods-for-progressive-multidimensional-scaling-ibb367akwh.pdf

Eigensolver methods for progressive multidimensional scaling of large data

In numerous application areas, general undirected graphs need to be drawn, and force-directed layout appears to be the most frequent choice We present an extensive experimental study showing that, if the goal is to represent the distances in a graph well, a combination of two simple algorithms based on variants of multidimensional scaling is to be preferred because of their efficiency, reliability, and even simplicity We also hope that details in the design of our study help advance experimental methodology in algorithm engineering and graph drawing, independent of the case at hand

/pdf/an-experimental-study-on-distance-based-graph-drawing-28cj14jnoc.pdf

An Experimental Study on Distance-Based Graph Drawing

We propose a visualization approach for large dynamic graph structures with high degree variation and low diameter. In particular, we reduce visual complexity by multiple modes of representation in a single-level visualization rather than abstractions of lower levels of detail. This is useful for non-interactive display and eases dynamic layout, which we address in the online scenario.

Our approach is illustrated on a family of large networks featuring all of the above structural characteristics, the physical Internet on the autonomous systems level over time.

/pdf/visualizing-internet-evolution-on-the-autonomous-systems-ybfv82jz9e.pdf

Visualizing internet evolution on the autonomous systems level

We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to the circumferences of a set of concentric circles around the origin. Such constraints frequently occur in the layout of social or policy networks, when structural centrality is mapped to geometric centrality, or when the primary intention of the layout is the display of the vicinity of a distinguished node. We extend stress majorization by a weighting scheme which imposes radial constraints on the layout but also tries to preserve as much information about the graph structure as possible.

More flexible radial layout

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