Resistance Distance, Information Centrality, Node Vulnerability and Vibrations in Complex Networks

Estrada, Ernesto; Hatano, Naomichi

doi:10.1007/978-1-84996-396-1_2

Cited by 22 publications

(10 citation statements)

References 35 publications

(57 reference statements)

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“…Interesting connections between message passing algorithms and electrical networks are discussed in [11]. In fact, electrical networks have also been put in connection with social networks, especially because of the notion of resistance distance [5].…”

Section: A Related Workmentioning

confidence: 99%

Message Passing Optimization of Harmonic Influence Centrality

Vassio

Fagnani

Frasca

et al. 2014

IEEE Trans. Control Netw. Syst.

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This paper proposes a new measure of node centrality in social networks, the Harmonic Influence Centrality, which emerges naturally in the study of social influence over networks.Using an intuitive analogy between social and electrical networks, we introduce a distributed message passing algorithm to compute the Harmonic Influence Centrality of each node. Although its design is based on theoretical results which assume the network to have no cycle, the algorithm can also be successfully applied on general graphs.

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Section: A Related Workmentioning

confidence: 99%

Message Passing Optimization of Harmonic Influence Centrality

Vassio

Fagnani

Frasca

et al. 2014

IEEE Trans. Control Netw. Syst.

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“…Furthermore, we have studied the Laplacian eigenvalue spectrum and the scaling of the second largest eigenvalue with system size, finding that the two systems are compatible. Using the findings from [14,29] we can infer that the structure of vibrational modes and relaxation properties produced by the model are similar to those found in biological proteins.…”

Section: Discussionmentioning

confidence: 63%

“…As two additional features roughly characterizing the dynamic properties of protein residue networks, we consider the distribution and scaling of Laplacian eigenvalues. The Laplacian of a network captures both its interaction topology and its relaxation and vibration properties [14,29]. If the PRN were made only of the central atoms, the Laplacian would exactly quantify the networks vibrational and relaxational modes.…”

Section: Distribution and Scaling Of Laplacian Eigenvaluesmentioning

confidence: 99%

Geometric constraints in protein folding

Molkenthin

Muehle

Mey

et al. 2018

Preprint

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The intricate three-dimensional geometries of protein tertiary structures underlie protein 2 function and emerge through a folding process from one-dimensional chains of amino acids. The exact 3 spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence 4 of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. 5 To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic 6 features of the folded structure, we propose a simple model of structure formation that takes into account 7 only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that 8 despite its simplicity, the model results in a network ensemble consistent with key overall features of the 9 ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as 10 available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors 11 a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum 12 and the scaling of the smallest relaxation time with chain length are all consistent between model and real 13 proteins. These results indicate that geometric constraints alone may already account for a number of 14 generic features of protein tertiary structures. Author summary 27 How proteins fold constitutes one of the most persistent, broad, and exciting open research questions at the 28 intersection of biology, chemistry, and physics. Which mechanisms induce a one-dimensional sequence of 29 amino acids to form into a complex three-dimensional (3D) structure? Proteins in their active 3D structure 30 impact most of the basic processes inside cells, including gene regulation, cell metabolism, and the creation 31 of protein structures themselves. Yet, a general rule about which conditions lead to which specific 3D protein 32 structures remains unknown to date. 33 Here, we demonstrate how a simple model that takes only fundamental geometric constraints into 34 account and otherwise assumes randomly paired connections, naturally generates an ensemble of folded 35 structures that exhibits many of its coarse scale features consistent with those of protein residue networks 36 resulting from tertiary structures of biological proteins. Specifically, we tested a set of more than 1000 37 biological proteins and model structures and extracted a range of ensemble properties, including the spatial 38 extension with chain size, the distribution of the number of interacting neighbors in the folded structure, the 39 spectrum of Laplacian eigenvalues, and the distribution of the dominant non-trivial eigenvalue. We found 40 1 of 14December 21, 2018 that all of those properties are consistent between the ensemble of biological protein residue networks and 41 the networks emerging in a self-organized way from the simple model. 42 These results indicate that coarse ensembl...

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“…This section will introduce a cyber‐physical technique to measure the grids risk to cyberattack based on the proposed security graph and contingency rankings. Graph resistance method has been applied to analyse the previously proposed algorithms to quantify the system vulnerability [34]. As identified in [11], attack difficulty is based on the length and quantity of paths between attackers and defenders.…”

Section: Attack Analysis Metricsmentioning

confidence: 99%

“…Previously, a very few works considered closeness centrality and betweenness centrality to find the criticality of the substation [20,36]. In this paper, the resistance distance is used as an index of node vulnerability to quantify an attack difficulty to travel various paths where a larger resistance distance is less vulnerable due to increased effort required for the attacker to traverse the security mechanisms [34]. Also, resistance distance acts as a key performance measure to study the robustness of a graph network when we have security mechanism insertion and/or removal.…”

Section: Resistance Distancementioning

confidence: 99%