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A MultiScale Algorithm for the Linear Arrangement Problem
 Proc. 28th Inter. Workshop on GraphTheoretic Concepts in Computer Science (WG’02), LNCS 2573
, 2002
"... Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a lineartime algorithm for this problem, based on the multiscale paradigm. Experimental results are similar to those of the best known approaches, while the running ti ..."
Abstract

Cited by 26 (4 self)
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Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a lineartime algorithm for this problem, based on the multiscale paradigm. Experimental results are similar to those of the best known approaches, while the running time is significantly better, enabling it to deal with much larger graphs. The paper contains a general multiscale construction, which may be used for a broader range of ordering problems.
Hierarchy Measure for Complex Networks
"... Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and d ..."
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Cited by 3 (0 self)
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Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of realworld networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the mreach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the
Visual Navigation Through Large Directed Graphs and Hypergraphs ∗ ABSTRACT
"... We describe Dynasty, a system for browsing large (possibly infinite) directed graphs and hypergraphs. Only a small subgraph is visible at any given time. We sketch how we lay out the visible subgraph, and how we update the layout smoothly and dynamically in an asynchronous environment. We also sketc ..."
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Cited by 2 (2 self)
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We describe Dynasty, a system for browsing large (possibly infinite) directed graphs and hypergraphs. Only a small subgraph is visible at any given time. We sketch how we lay out the visible subgraph, and how we update the layout smoothly and dynamically in an asynchronous environment. We also sketch our user interface for browsing and annotating such graphs—in particular, how we try to make keyboard navigation usable.
AxisbyAxis Stress Minimization
 Proceedings of Graph Drawing 2003
, 2003
"... Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. They were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensio ..."
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Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. They were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensional scaling.