Convex skeletons of complex networks

Šubelj, Lovro

doi:10.1098/rsif.2018.0422

Cited by 6 publications

(7 citation statements)

References 62 publications

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“…Firstly, as already mentioned above, different collaboration networks turn out to be rather convex (Marc and Šubelj, 2018;Šubelj, 2018), which is in contrast to paper citation and other bibliographic networks. Convex skeletons should therefore represent their meaningful abstraction, which is not the case for the latter.…”

Section: Introductionmentioning

confidence: 93%

Convexity in scientific collaboration networks

Šubelj

Fiala

Ciglarič

et al. 2019

Journal of Informetrics

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Convexity in a network (graph) has been recently defined as a property of each of its subgraphs to include all shortest paths between the nodes of that subgraph. It can be measured on the scale [0, 1] with 1 being assigned to fully convex networks. The largest convex component of a graph that emerges after the removal of the least number of edges is called a convex skeleton. It is basically a tree of cliques, which has been shown to have many interesting features. In this article the notions of convexity and convex skeletons in the context of scientific collaboration networks are discussed. More specifically, we analyze the co-authorship networks of Slovenian researchers in computer science, physics, sociology, mathematics, and economics and extract convex skeletons from them. We then compare these convex skeletons with the residual graphs (remainders) in terms of collaboration frequency distributions by various parameters such as the publication year and type, co-authors' birth year, status, gender, discipline, etc. We also show the top-ranked scientists by four basic centrality measures as calculated on the original networks and their skeletons and conclude that convex skeletons may help detect influential scholars that are hardly identifiable in the original collaboration network. As their inherent feature, convex skeletons retain the properties of collaboration networks. These include high-level structural properties but also 2 the fact that the same authors are highlighted by centrality measures. Moreover, the most important ties and thus the most important collaborations are retained in the skeletons.

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Section: Introductionmentioning

confidence: 93%

Convexity in scientific collaboration networks

Šubelj

Fiala

Ciglarič

et al. 2019

Journal of Informetrics

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“…A spanning tree can be seen as a technique for revealing a network backbone or skeleton (Coscia and Neffke, 2017;Šubelj, 2018), with applications in network visualization and link prediction. Furthermore, a spanning is one of the simplest approaches for network simplification or sampling (Leskovec and Faloutsos, 2006;Blagus et al, 2017).…”

Section: Applications Of Spanning Treesmentioning

confidence: 99%

“…Techniques to alleviate this issue include network simplification or sampling (Leskovec and Faloutsos, 2006;Hamann et al, 2016;Blagus et al, 2017), and revealing the so-called network backbone or skeleton (Grady et al, 2012;Coscia and Neffke, 2017;Šubelj, 2018). These approaches try to reduce the size of a network in a way that the network still retains many of its structural properties.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for spanning trees of unweighted networks

Šubelj¹

2022

Preprint

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Spanning tree of a network or a graph is a subgraph connecting all the nodes with the minimum number of edges. Spanning tree retains the connectivity of a network and possibly other structural properties, and is one of the simplest techniques for network simplification or sampling, and for revealing its backbone or skeleton. The Prim's algorithm and the Kruskal's algorithm are well known algorithms for computing a spanning tree of a weighted network. In this paper, we study the performance of these algorithms on unweighted networks, and compare them to different priority-first search algorithms. We show that the distances between the nodes and the diameter of a network are best preserved by an algorithm based on the breadth-first search node traversal. The algorithm computes a spanning tree with properties of a balanced tree and a power-law node degree distribution. We support our results by experiments on synthetic graphs and more than a thousand real networks, and demonstrate different practical applications of computed spanning trees. We conclude that, if a spanning tree is supposed to retain the distances between the nodes or the diameter of an unweighted network, then the breadth-first search algorithm should be the preferred choice.

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“…Since convexity is a property inherent to real networks, the research may prove useful in various applications of network classification as well as in distinguishing the networks from random graphs [5]. Another direction for research involves community detection in networks based on their convex skeleton [6], which can be viewed as a generalization of a spanning tree. The research results might also be applied to the problem of finding the optimal subgraph of roads in transportation networks [5], [6], active and online node classification [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Fast Approximate Convex Hull Construction in Networks via Node Embedding

Gavrilev

Makarov²

2023

IEEE Access

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Geodesic convexity in networks is an intrinsic property of graphs. It aids in distinguishing between real-world networks and random graphs. One possible application is recommending new connections in a collaborative network by searching for them in the so-called convex hull, which is a minimal subgraph containing all the shortest paths between its nodes. However, the existing algorithms for constructing convex hulls from subsets of nodes involve extensive search over subgraphs and have poor scalability. Thus, they become inapplicable to large graphs such as social networks. In this paper, we propose a new approach for fast convex hull construction for a subset of nodes on a network using graph embeddings. We apply the well-known convexity concept in embedding space to a similar problem for geometric learning on a graph, optimizing the process of finding all the shortest paths in the induced subgraph. To preserve the metric characteristics of a network, we train a graph neural network with an L1-distance loss. As a result, the trained model enables us to approximately verify the convexity of subgraphs in linear time, contrary to the previous approaches, which have cubic complexity.

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Convex skeletons of complex networks

Cited by 6 publications

References 62 publications

Convexity in scientific collaboration networks

Convexity in scientific collaboration networks

Algorithms for spanning trees of unweighted networks

Fast Approximate Convex Hull Construction in Networks via Node Embedding

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