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Documents authored by Salas, Jorge


Document
Absolute Expressiveness of Subgraph-Based Centrality Measures

Authors: Andreas Pieris and Jorge Salas

Published in: LIPIcs, Volume 255, 26th International Conference on Database Theory (ICDT 2023)


Abstract
In graph-based applications, a common task is to pinpoint the most important or "central" vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called centrality measures have been proposed in the literature. Such measures assess which vertices in a graph are the most important ones by analyzing the structure of the underlying graph. A family of centrality measures that are suited for graph databases has been recently proposed by relying on the following simple principle: the importance of a vertex in a graph is relative to the number of "relevant" connected subgraphs surrounding it; we refer to the members of this family as subgraph-based centrality measures. Although it has been shown that such measures enjoy several favourable properties, their absolute expressiveness remains largely unexplored. The goal of this work is to precisely characterize the absolute expressiveness of the family of subgraph-based centrality measures by considering both directed and undirected graphs. To this end, we characterize when an arbitrary centrality measure is a subgraph-based one, or a subgraph-based measure relative to the induced ranking. These characterizations provide us with technical tools that allow us to determine whether well-established centrality measures are subgraph-based. Such a classification, apart from being interesting in its own right, gives useful insights on the structural similarities and differences among existing centrality measures.

Cite as

Andreas Pieris and Jorge Salas. Absolute Expressiveness of Subgraph-Based Centrality Measures. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 9:1-9:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{pieris_et_al:LIPIcs.ICDT.2023.9,
  author =	{Pieris, Andreas and Salas, Jorge},
  title =	{{Absolute Expressiveness of Subgraph-Based Centrality Measures}},
  booktitle =	{26th International Conference on Database Theory (ICDT 2023)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-270-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{255},
  editor =	{Geerts, Floris and Vandevoort, Brecht},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2023.9},
  URN =		{urn:nbn:de:0030-drops-177516},
  doi =		{10.4230/LIPIcs.ICDT.2023.9},
  annote =	{Keywords: Graph centrality measures, ranking, expressiveness}
}
Document
How Do Centrality Measures Choose the Root of Trees?

Authors: Cristian Riveros, Jorge Salas, and Oskar Skibski

Published in: LIPIcs, Volume 255, 26th International Conference on Database Theory (ICDT 2023)


Abstract
Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused on classes of centrality measures. In this work, we provide a different approach by focusing on classes of graphs instead of classes of measures to understand the underlying principles among various measures. More precisely, we study the class of trees. We observe that even in the case of trees, there is no consensus on which node should be selected as the most central. To analyze the behavior of centrality measures on trees, we introduce a property of tree rooting that states a measure selects one or two adjacent nodes as the most important, and the importance decreases from them in all directions. This property is satisfied by closeness centrality but violated by PageRank. We show that, for several centrality measures that root trees, the comparison of adjacent nodes can be inferred by potential functions that assess the quality of trees. We use these functions to give fundamental insights on rooting and derive a characterization explaining why some measure root trees. Moreover, we provide an almost linear time algorithm to compute the root of a graph by using potential functions. Finally, using a family of potential functions, we show that many ways of tree rooting exist with desirable properties.

Cite as

Cristian Riveros, Jorge Salas, and Oskar Skibski. How Do Centrality Measures Choose the Root of Trees?. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 12:1-12:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{riveros_et_al:LIPIcs.ICDT.2023.12,
  author =	{Riveros, Cristian and Salas, Jorge and Skibski, Oskar},
  title =	{{How Do Centrality Measures Choose the Root of Trees?}},
  booktitle =	{26th International Conference on Database Theory (ICDT 2023)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-270-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{255},
  editor =	{Geerts, Floris and Vandevoort, Brecht},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2023.12},
  URN =		{urn:nbn:de:0030-drops-177545},
  doi =		{10.4230/LIPIcs.ICDT.2023.12},
  annote =	{Keywords: Databases, centrality measures, data centrality, graph theory, tree structures}
}
Document
A Family of Centrality Measures for Graph Data Based on Subgraphs

Authors: Cristian Riveros and Jorge Salas

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)


Abstract
We present the theoretical foundations of a new approach in centrality measures for graph data. The main principle of our approach is very simple: the more relevant subgraphs around a vertex, the more central it is in the network. We formalize the notion of "relevant subgraphs" by choosing a family of subgraphs that, give a graph G and a vertex v in G, it assigns a subset of connected subgraphs of G that contains v. Any of such families defines a measure of centrality by counting the number of subgraphs assigned to the vertex, i.e., a vertex will be more important for the network if it belongs to more subgraphs in the family. We show many examples of this approach and, in particular, we propose the all-subgraphs centrality, a centrality measure that takes every subgraph into account. We study fundamental properties over families of subgraphs that guarantee desirable properties over the corresponding centrality measure. Interestingly, all-subgraphs centrality satisfies all these properties, showing its robustness as a notion for centrality. Finally, we study the computational complexity of counting certain families of subgraphs and show a polynomial time algorithm to compute the all-subgraphs centrality for graphs with bounded tree width.

Cite as

Cristian Riveros and Jorge Salas. A Family of Centrality Measures for Graph Data Based on Subgraphs. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 23:1-23:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{riveros_et_al:LIPIcs.ICDT.2020.23,
  author =	{Riveros, Cristian and Salas, Jorge},
  title =	{{A Family of Centrality Measures for Graph Data Based on Subgraphs}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.23},
  URN =		{urn:nbn:de:0030-drops-119474},
  doi =		{10.4230/LIPIcs.ICDT.2020.23},
  annote =	{Keywords: Graph data, graph centrality, centrality measures}
}
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