Network topology measures

Kincaid, Rex K.; Phillips, David J.

doi:10.1002/wics.180

Cited by 6 publications

(7 citation statements)

References 43 publications

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“…This measure is widely used in scale-free networks and is generalized by the Randic index [64,65]. In particular, s(G) = x,y∈V S xy is called a scale-free metric and is used as a measure of scale-freeness of the graph [66].…”

Section: Comparison With Other Link Prediction Methodsmentioning

confidence: 99%

Symmetry-driven network reconstruction through pseudobalanced coloring optimization

Leifer,

Phillips,

Sorrentino

et al. 2021

Preprint

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Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of complex biological systems. Network symmetries can be determined by finding a balanced coloring of the graph, which is a node partition in which each cluster of nodes receives the same information (color) from the rest of the graph.Networks based on real systems, however, are built on experimental data which are inherently incomplete, due to missing links, collection errors, and natural variations within specimens of the same biological species. Therefore, a method to find pseudosymmetries and repair networks based on those symmetries is important when analyzing real world networks. In this paper we introduce the pseudobalanced coloring (PBCIP) problem, and provide an integer programming formulation which (a) calculates a pseudobalanced coloring of the graph taking into account the missing data, and (b) optimally repairs the graph with the minimal number of added/removed edges to maximize the symmetry of the graph. We apply our formulation to the C. elegans connectome to find pseudocoloring and the optimal graph repair. Our solution compares well with a manually curated ground-truth C. elegans graph as well as solutions generated by other methods of missing link prediction. Furthermore, we provide an extension of the algorithm using Bender's decomposition that allows our formulation to be applied to larger networks.

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Section: Comparison With Other Link Prediction Methodsmentioning

confidence: 99%

Symmetry-driven network reconstruction through pseudobalanced coloring optimization

Leifer,

Phillips,

Sorrentino

et al. 2021

Preprint

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show abstract

“…For the measurement of information from vector data, Jie, Min, Feng, and Zheng () studied point and surface information measurements and the transfer model of geometric information at different scales. Kincaid and Phillips () focused on identifying network‐invariant functions, measuring related topological features (such as connectivity and sparsity), and studying the network topology and its relationship with global and local network structures. Huimin () proposed a measurement of map topological information, which considers the difference in adjacency of map symbols.…”

Section: Introductionmentioning

confidence: 99%

An improved measuring method for the information entropy of network topology

Liu

2018

Transactions in GIS

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The measurement of network topologies is of great significance to the multi‐scale expression and generalization of maps. The problem encountered in existing metrics is whether to use the approach of measuring a single type of information or measuring the overall information; however, redundancy can be calculated. In view of these problems, this article selects three types of information metrics that express compactness, heterogeneity, and discreteness in a network topology. The measurement model has been simplified, and the calculation has been improved. By comparing various methods and measuring the information entropy of area road networks, the simplicity and validity of the improved method are verified.

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“…In particular, we have the following results: We describe the first strongly polynomial algorithm to solve the generalized minimum Randić index problem. Although we typically consider the case where α = 1, our results and algorithms apply to any non‐zero α . We define the variant where S b is restricted to connected subgraphs as the connected generalized Randić index problem , an important property for many applications .We prove that the connected generalized Randić index problem is APX‐hard, that is, it is even NP‐hard to approximate. We define the variant where G is the complete graph on n vertices as the generalized Randić index degree sequence problem . We conjecture that the connected generalized Randić index degree sequence problem is NP‐hard even if α is restricted to one.…”

Section: Introductionmentioning

confidence: 99%

“…Although we typically consider the case where α = 1, our results and algorithms apply to any non-zero α. • We define the variant where S b is restricted to connected subgraphs as the connected generalized Randić index problem, an important property for many applications [21].We prove that the connected generalized Randić index problem is APX-hard, that is, it is even NP-hard to approximate. • We define the variant where G is the complete graph on n vertices as the generalized Randić index degree sequence…”

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confidence: 95%

Algorithms and complexity results for finding graphs with extremal Randić index

et al. 2016

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We show that finding a subgraph realization with the minimum generalized Randić index for a given base graph and degree sequence is solvable in polynomial time by formulating the problem as the minimum weight perfect b-matching problem of Edmonds (J Res Natl Bur Stand 69B (1965), 125-130). However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight perfect b-matching problem subject to a connectivity constraint is shown to be NPhard. For instances in which the optimal solution to the minimum Randić index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. Although we focus on finding graph realizations with minimum Randić index, our results extend to finding graph realizations with maximum Randić index as well. Applications of the Randić index are provided to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia.

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Network topology measures

Cited by 6 publications

References 43 publications

Symmetry-driven network reconstruction through pseudobalanced coloring optimization

Symmetry-driven network reconstruction through pseudobalanced coloring optimization

An improved measuring method for the information entropy of network topology

Algorithms and complexity results for finding graphs with extremal Randić index

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