Separator-based data reduction for signed graph balancing

Hüffner, Falk; Betzler, Nadja; Niedermeier, Rolf

doi:10.1007/s10878-009-9212-2

Cited by 43 publications

(108 citation statements)

References 53 publications

(62 reference statements)

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“…The frustration index can be computed in polynomial time for planar graphs [56,53]. In general graphs; however, the frustration index is even NP-hard to approximate within any constant factor [53]. There has been a lack of systematic investigations for computing the exact frustration index of largescale networks [6,7].…”

Section: Computing the Frustration Indexmentioning

confidence: 99%

Balance and frustration in signed networks

Aref

2018

Journal of Complex Networks

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The frustration index is a key measure for analysing signed networks, which has been underused due to its computational complexity. We use an exact optimisation-based method to analyse frustration as a global structural property of signed networks coming from diverse application areas. In the classic friendenemy interpretation of balance theory, a by-product of computing the frustration index is the partitioning of nodes into two internally solidary but mutually hostile groups. The main purpose of this paper is to present general methodology for answering questions related to partial balance in signed networks, and apply it to a range of representative examples that are now analysable because of advances in computational methods. We provide exact numerical results on social and biological signed networks, networks of formal alliances and antagonisms between countries, and financial portfolio networks. Molecular graphs of carbon and Ising models are also considered. The purpose served by exploring several problems in this paper is to propose a single general methodology for studying signed networks and to demonstrate its relevance to applications. We point out several mistakes in the signed networks literature caused by inaccurate computation, implementation errors or inappropriate measures. Cornyn (R-TX) Corzine (D-NJ) Craig (R-ID) DeWine (R-OH) Dodd (D-CT) Domenici (R-NM) Durbin (D-IL) Edwards (D-NC) Ensign (R-NV)

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Section: Computing the Frustration Indexmentioning

confidence: 99%

Balance and frustration in signed networks

Aref

2018

Journal of Complex Networks

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“…Signed Max-Cut finds applications in, e.g., modelling social networks [19], statistical physics [2], portfolio risk analysis [20], and VLSI design [4]. The dual parameterization of Signed Max-Cut by the number of edge deletions was also shown to be fixed-parameter tractable [21].…”

Section: Introductionmentioning

confidence: 99%

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

Etscheid

Mnich

2017

Algorithmica

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The maximum cut problem in graphs and its generalizations are fundamental combinatorial problems. Several of these cut problems were recently shown to be fixed-parameter tractable and admit polynomial kernels when parameterized above the tight lower bound measured by the size and order of the graph. In this paper we continue this line of research and considerably improve several of those results: Dedicated to the 60th birthday of Gregory Gutin. All presented kernels can be computed in time O(km). Supported by ERC Starting Grant 306465 (BeyondWorstCase

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“…39 For approximating this distance, di®erent methods are presented. [40][41][42][43] Iacono et al 40 have switched the sign of links so that the number of negative links becomes minimum in the graph. Afterwards, one spanning tree which possibly does not pass through negative edge is found.…”

Section: Structural Balancementioning

confidence: 99%

Introducing a more realistic model for opinion formation considering instability in social structure

Salehi

Taghiyareh

2016

Int. J. Mod. Phys. C

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Opinion formation is a process through which interactions of individuals and dynamism of their opinions in e®ect of neighbors are modeled. In this paper, in an e®ort to model the opinion formation more realistically, we have introduced a model that considers the role of network structure in opinion dynamics. In this model, each individual changes his opinion in a way so as to decrease its di®erence with the opinion of trusted neighbors while he intensi¯es his dissention with the untrusted ones. Considering trust/distrust relations as a signed network, we have de¯ned a structural indicator which shows the degree of instability in social structure and is calculated based on the structural balance theory. It is also applied as feedback to the opinion formation process a®ecting its dynamics. Our simulation results show formation of a set of clusters containing individuals holding opinions having similar values. Also, the opinion value of each individual is far from the ones of distrusted neighbors. Since this model considers distrust and instability of relations in society, it can o®er a more realistic model of opinion formation.

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Separator-based data reduction for signed graph balancing

Cited by 43 publications

References 53 publications

Balance and frustration in signed networks

Balance and frustration in signed networks

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

Introducing a more realistic model for opinion formation considering instability in social structure

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