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Structural Similarity in Graphs [chapter]

Ulrik Brandes, Jürgen Lerner
2004 Lecture Notes in Computer Science  
Standard methods for role assignment partition the vertex set of a graph in such a way that vertices in the same class can be considered to have equivalent roles in the graph.  ...  In this paper we introduce the concept of structural similarity by relaxation of equitable partitions, thus providing a theoretical foundation for similarity measures which enjoys desirable properties  ...  It is N P-complete to decide for two graphs G and R whether there is 1. a regular role assignment for G with given role graph R, 2. an equitable partition for G with quotient R.  ... 
doi:10.1007/978-3-540-30551-4_18 fatcat:enahsz3pnbgpjcmypwvi3x6ok4

Similarity in Semantic Graphs: Combining Structural, Literal, and Ontology-based Measures

Lindsey Vanderlyn, Carl Andersen, Plamen Petrov
2015 Semantic Technologies for Intelligence, Defense, and Security  
As these graphs become more popular for storing large quantities of data, it is important to have methods of determining similarity between nodes in the graph.  ...  This paper extends previous structural similarity algorithms by taking advantage of meaning contained in a graph's literals and the graph's ontology and allowing users to control how much each type of  ...  With SSDM+, we combine both the literal and ontological similarity into a larger structural approach.  ... 
dblp:conf/stids/VanderlynAP15 fatcat:jwkmcijvszcwzgtt3p4z35tr7q

Role Discovery in Networks

Ryan A. Rossi, Nesreen K. Ahmed
2015 IEEE Transactions on Knowledge and Data Engineering  
We briefly revisit these early notions and instead propose a more general formulation of roles based on the similarity of a feature representation (in contrast to the graph representation).  ...  We also propose a flexible framework for discovering roles using the notion of similarity on a feature-based representation.  ...  In general, these approaches use some form of structural similarity for features. Intuitively, two nodes share the same role, if they have similar features.  ... 
doi:10.1109/tkde.2014.2349913 fatcat:3qmmwr3hq5divmr57khcpy6uey

Local, global and scale-dependent node roles [article]

Michael Scholkemper, Michael T. Schaub
2021 arXiv   pre-print
Traditionally, such exact node equivalences have been defined either in terms of the one hop neighborhood of a node, or in terms of the global graph structure.  ...  plays within a social system, but have since then been of independent interest for graph-based learning tasks.  ...  First, we formalize exact node roles with a scale parameter, describing up to what distance the graph structure surrounding a node should be considered when assigning node roles.  ... 
arXiv:2105.12598v1 fatcat:4fvxquwhrbfepoifx5gywz26nu

Structural Similarity: Spectral Methods for Relaxed Blockmodeling

Ulrik Brandes, Jürgen Lerner
2010 Journal of Classification  
In this paper we propose the concept of structural similarity as a relaxation of blockmodeling in social network analysis.  ...  Most previous approaches attempt to relax the constraints on partitions, for instance, that of being a structural or regular equivalence to being approximately structural or regular, respectively.  ...  Our Approach As it has been outlined in the introduction, structural similarities relax the condition that role assignments must be discrete vertex partitions but keep the requirement for exact regular  ... 
doi:10.1007/s00357-010-9062-8 fatcat:jujk2zlmnbekdjjwi5667mr5re

Group-Level Analysis and Visualization of Social Networks [chapter]

Michael Baur, Ulrik Brandes, Jürgen Lerner, Dorothea Wagner
2009 Lecture Notes in Computer Science  
These methods include the computation of densely connected groups (clustering) and the computation of structural roles and positions (blockmodeling or role assignment, see Sect. 2).  ...  In order to abstract from the particular application context, we assume that networks are represented by graphs G = (V, E), where V is a set of vertices, encoding the actors, and E is a set of edges (also  ...  The Role-Assignment Problem For a given graph there is a huge set of structural similarities.  ... 
doi:10.1007/978-3-642-02094-0_16 fatcat:rdyz7ydvpvefbhcfodbfq2sdrm

Preserving structural properties in anonymization of social networks

Amirreza Masoumzadeh, James Joshi
2010 Proceedings of the 6th International ICST Conference on Collaborative Computing: Networking, Applications, Worksharing  
We propose an approach for enhancing anonymization techniques that preserves the structural semantics of the original social network by using the notion of roles and positions.  ...  However, such approaches introduce a large amount of distortion to the original social network graphs, thus raising serious questions about their utility for useful social network analysis.  ...  Hence, we need a different approach to enhance it for preserving role structure. We propose to substitute the gain function in Algorithm 2 with a new similarity gain measure.  ... 
doi:10.4108/icst.collaboratecom.2010.7 dblp:conf/colcom/MasoumzadehJ10 fatcat:oh2h5lbozjgmpmzwijahg2j254

Ontology Mapping via Structural and Instance-based Similarity Measures

Konstantin Todorov, Peter Geibel
2008 International Semantic Web Conference  
It combines structural and instance-based approaches to reduce the terminological and conceptual ontology heterogeneity.  ...  The paper presents an overview of a novel procedure for mapping hierarchical ontologies, populated with properly classified text documents.  ...  In addition to the structural approach, we employ two extensional methods for deriving concepts similarity assertions.  ... 
dblp:conf/semweb/TodorovG08 fatcat:rb2gidf35fggpj42gknws2fsoy

A neighborhood-based approach for clustering of linked document collections

Ralitsa Angelova, Stefan Siersdorfer
2006 Proceedings of the 15th ACM international conference on Information and knowledge management - CIKM '06  
Our approach is based on iterative relaxation of cluster assignments, and can be built on top of any clustering algorithm (e.g., k-means or DBSCAN).  ...  In contrast to traditional clustering, we study the clustering problem in the light of available link structure information for the data set (e.g., hyperlinks among web documents or co-authorship among  ...  A similar approach was used in [22] for document classification.  ... 
doi:10.1145/1183614.1183726 dblp:conf/cikm/AngelovaS06 fatcat:5y7g2ty7qvdgtiavqpqso3ifo4

An Automorphic Distance Metric and its Application to Node Embedding for Role Mining [article]

Víctor Martínez, Fernando Berzal, Juan-Carlos Cubero
2018 arXiv   pre-print
Instead, a relaxed definition in terms of similarity or distance is commonly used to compute the degree to which two nodes are equivalent.  ...  Role is a fundamental concept in the analysis of the behavior and function of interacting entities represented by network data. Role discovery is the task of uncovering hidden roles.  ...  In practice, these equivalences are relaxed to similarities, allowing two nodes to play the same role by partially satisfying the constraints imposed by the mathematical definition of structural, automorphic  ... 
arXiv:1712.06979v2 fatcat:3alz4bi4pbdlzpwfpqoxszoboe

The analysis of split graphs in social networks based on the k-cardinality assignment problem

Ivan Belik
2016 International Journal of Network Science  
Based on the semi-Lagrangean relaxation for the k-cardinality assignment problem, we show the way of minimising socially risky interactions between cliques and independent sets within social networks.  ...  In terms of social networks, split graphs correspond to the variety of interpersonal and intergroup relations.  ...  Next, we introduced the algorithm for the risk of trust minimisation in split graphs based on our approach of the semi-Lagrangean relaxation for the k-cardinality problem.  ... 
doi:10.1504/ijns.2016.073557 fatcat:xfbpwii2jrh25nnt7yvaigqxou

A Combinatorial Approach to Role Discovery

Albert Arockiasamy, Aristides Gionis, Nikolaj Tatti
2016 2016 IEEE 16th International Conference on Data Mining (ICDM)  
A combinatorial approach to role discovery Master's Thesis EspooWe provide a new formulation for the problem of role discovery in graphs.  ...  Our definition is structural and recursive: two vertices should be assigned to the same role if the roles of their neighbors, when viewed as multi-sets, are similar enough.  ...  Based on this relaxation, role discovery can be defined as a process that takes a network graph as input, identifies the equivalent nodes, clusters sets of nodes with similar structural patterns and assigns  ... 
doi:10.1109/icdm.2016.0091 dblp:conf/icdm/ArockiasamyGT16 fatcat:uvntgd475ze7hepdwfhbw334p4

Variational Bayes in Private Settings (VIPS) (Extended Abstract)

James R. Foulds, Mijung Park, Kamalika Chaudhuri, Max Welling
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method.  ...  In the full paper we extend our method to a broad class of models, including Bayesian logistic regression and sigmoid belief networks.  ...  kj , X) consistency score (6) This approach estimates matchings between dissimilar graphs by composition along a path of similar graphs.  ... 
doi:10.24963/ijcai.2020/694 dblp:conf/ijcai/YanYH20 fatcat:pc4nelo7gzfmvmsiym3ohwspxa

Graph-Based Methods for Vision: A Yorkist Manifesto [chapter]

Edwin Hancock, Richard C. Wilson
2002 Lecture Notes in Computer Science  
The first of these is that we have a probabilistic measure of graph similarity, which naturally plays the role of a fitness function [8] .  ...  Much of the work described above adopts a heuristic or goal directed approach to measuring graph similarity.  ... 
doi:10.1007/3-540-70659-3_3 fatcat:magj2vz4hfbcdni4krsnvy7ru4

A Novel Graph-based Approach for Determining Molecular Similarity [article]

Maritza Hernandez, Arman Zaribafiyan, Maliheh Aramon, Mohammad Naghibi
2016 arXiv   pre-print
To account for noise, we relax the definition of similarity using the maximum weighted co-k-plex relaxation method, which allows dissimilarities among graphs up to a predetermined level.  ...  In this paper, we tackle the problem of measuring similarity among graphs that represent real objects with noisy data.  ...  This research was supported in part by 1QBit and the Mitacs Accelerate and Elevate programs.  ... 
arXiv:1601.06693v1 fatcat:f2am23s4wbh55ojl3ds5ihha4i
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