7,119 research outputs found
NodeTrix: Hybrid Representation for Analyzing Social Networks
The need to visualize large social networks is growing as hardware
capabilities make analyzing large networks feasible and many new data sets
become available. Unfortunately, the visualizations in existing systems do not
satisfactorily answer the basic dilemma of being readable both for the global
structure of the network and also for detailed analysis of local communities.
To address this problem, we present NodeTrix, a hybrid representation for
networks that combines the advantages of two traditional representations:
node-link diagrams are used to show the global structure of a network, while
arbitrary portions of the network can be shown as adjacency matrices to better
support the analysis of communities. A key contribution is a set of interaction
techniques. These allow analysts to create a NodeTrix visualization by dragging
selections from either a node-link or a matrix, flexibly manipulate the
NodeTrix representation to explore the dataset, and create meaningful summary
visualizations of their findings. Finally, we present a case study applying
NodeTrix to the analysis of the InfoVis 2004 coauthorship dataset to illustrate
the capabilities of NodeTrix as both an exploration tool and an effective means
of communicating results
StructMatrix: large-scale visualization of graphs by means of structure detection and dense matrices
Given a large-scale graph with millions of nodes and edges, how to reveal
macro patterns of interest, like cliques, bi-partite cores, stars, and chains?
Furthermore, how to visualize such patterns altogether getting insights from
the graph to support wise decision-making? Although there are many algorithmic
and visual techniques to analyze graphs, none of the existing approaches is
able to present the structural information of graphs at large-scale. Hence,
this paper describes StructMatrix, a methodology aimed at high-scalable visual
inspection of graph structures with the goal of revealing macro patterns of
interest. StructMatrix combines algorithmic structure detection and adjacency
matrix visualization to present cardinality, distribution, and relationship
features of the structures found in a given graph. We performed experiments in
real, large-scale graphs with up to one million nodes and millions of edges.
StructMatrix revealed that graphs of high relevance (e.g., Web, Wikipedia and
DBLP) have characterizations that reflect the nature of their corresponding
domains; our findings have not been seen in the literature so far. We expect
that our technique will bring deeper insights into large graph mining,
leveraging their use for decision making.Comment: To appear: 8 pages, paper to be published at the Fifth IEEE ICDM
Workshop on Data Mining in Networks, 2015 as Hugo Gualdron, Robson Cordeiro,
Jose Rodrigues (2015) StructMatrix: Large-scale visualization of graphs by
means of structure detection and dense matrices In: The Fifth IEEE ICDM
Workshop on Data Mining in Networks 1--8, IEE
Graph edit distance from spectral seriation
This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems
Perfect Elimination Orderings for Symmetric Matrices
We introduce a new class of structured symmetric matrices by extending the
notion of perfect elimination ordering from graphs to weighted graphs or
matrices. This offers a common framework capturing common vertex elimination
orderings of monotone families of chordal graphs, Robinsonian matrices and
ultrametrics. We give a structural characterization for matrices that admit
perfect elimination orderings in terms of forbidden substructures generalizing
chordless cycles in graphs.Comment: 16 pages, 3 figure
Requirements for Topology in 3D GIS
Topology and its various benefits are well understood within the context of 2D Geographical Information Systems. However, requirements in three-dimensional (3D) applications have yet to be defined, with factors such as lack of users' familiarity with the potential of such systems impeding this process. In this paper, we identify and review a number of requirements for topology in 3D applications. The review utilises existing topological frameworks and data models as a starting point. Three key areas were studied for the purposes of requirements identification, namely existing 2D topological systems, requirements for visualisation in 3D and requirements for 3D analysis supported by topology. This was followed by analysis of application areas such as earth sciences and urban modelling which are traditionally associated with GIS, as well as others including medical, biological and chemical science. Requirements for topological functionality in 3D were then grouped and categorised. The paper concludes by suggesting that these requirements can be used as a basis for the implementation of topology in 3D. It is the aim of this review to serve as a focus for further discussion and identification of additional applications that would benefit from 3D topology. © 2006 The Authors. Journal compilation © 2006 Blackwell Publishing Ltd
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Social Network Analysis with sna
Modern social network analysis---the analysis of relational data arising from social systems---is a computationally intensive area of research. Here, we provide an overview of a software package which provides support for a range of network analytic functionality within the R statistical computing environment. General categories of currently supported functionality are described, and brief examples of package syntax and usage are shown.
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