CiSE: A Circular Spring Embedder Layout Algorithm

Abstract

We present a new algorithm for automatic layout of clustered graphs using a circular style. The algorithm tries to determine optimal location and orientation of individual clusters intrinsically within a modified spring embedder. Heuristics such as reversal of the order of nodes in a cluster and swap of neighboring node pairs in the same cluster are employed intermittently to further relax the spring embedder system, resulting in reduced inter-cluster edge crossings. Unlike other algorithms generating circular drawings, our algorithm does not require the quotient graph to be acyclic, nor does it sacrifice the edge crossing number of individual clusters to improve respective positioning of the clusters. Moreover, it reduces the total area required by a cluster by using the space inside the associated circle. Experimental results show that the execution time and quality of the produced drawings with respect to commonly accepted layout criteria are quite satisfactory, surpassing previous algorithms. The algorithm has also been successfully implemented and made publicly available as part of a compound and clustered graph editing and layout tool named CHISIO.

Multilayer network simplification: Approaches, models and methods

“…Given the rising complexity and volume of current networks, graph embedding techniques represent an essential tool to reduce the size of the network, capture meaningful patterns and thus build visual representations which can easily convey properties and structural information of complex networks. Traditional visualization algorithms seek to find a compromise between clarity of structural characteristics and aesthetic requirements such as fixed edge lengths or minimal edge crossing (e.g., [58,102,31]) while resorting to multidimensional scaling to find a low-dimensional representation of high dimensional data, with the goal of preserving pairwise dissimilarities in terms of Euclidean distance [12,3].…”

GiViP: A Visual Profiler for Distributed Graph Processing Systems

“…3(b). The main novelties introduced by our enhanced chord diagram are: (i) the use of heuristics for crossing minimization inspired by the literature on circular layouts (see, e.g., [9,21,23,56]), and (ii) a bimodal orientation of the edges in which the incoming and the outgoing edges of each vertex form two contiguous intervals [22].…”

Kernel-based embeddings for large graphs with centrality constraints

“…Traditional visualization algorithms on small graphs tend to em phasize aesthetics like minimal edge crossing over underlying struc tural patterns, see e.g., [8,17,21]. As a result, they are ill-equipped to visualize larger graphs.…”

“…(8) into the equality constraint in(6), one obtains the closed-form per-iteration update x� = { 1I :!II J(Ci), if Ilvil1 2 Xr denote the embedding matrix after T BCD iterations, the operation X = (I -N-1 11 T)xr centers {XD: 1 to the origin in order to satisfy the shift invariance property of the embedding. Algo rithm I summarizes the steps outlined for the centrality-constrained graph embedding scheme.…”