Robustness of Regular Caterpillars

2017 ◽  
Vol 28 (07) ◽  
pp. 835-841 ◽  
Author(s):  
Aysun Aytaç ◽  
Zeynep Nihan Odabaş Berberler
Keyword(s):  
Computer Networks ◽  
Network Topology ◽  
Network Robustness ◽  
Graph Theoretic ◽  
Theoretic Concept

Robustness of the network topology is a key aspect in the design of computer networks. Vertex residual closeness is a new graph-theoretic concept defined as a measure of network robustness. In this model, edges are perfectly reliable and the vertices fail independently of each other. In this paper, vertex residual closeness of paths and regular caterpillars are calculated by giving an insight of how to evaluate the vertex residual closeness of path-like graphs.

Extremal Results on Vertex and Link Residual Closeness

2021 ◽  
pp. 1-21
Author(s):  
Bo Zhou ◽  
Zhenan Li ◽  
Haiyan Guo
Keyword(s):  
Computer Networks ◽  
Network Topology ◽  
Network Robustness ◽  
Unicyclic Graphs ◽  
Graph Theoretic ◽  
Theoretic Concept

Robustness of the network topology is a key aspect in the design of computer networks. Vertex (Link, respectively) residual closeness is a new graph-theoretic concept defined as a measure of network robustness due to the failure of individual vertices (links, respectively). In this paper, we identify the trees and unicyclic graphs with the first a few smallest vertex residual closeness, and determine the graphs that minimize or maximize the vertex (link, respectively) residual closeness over some classes of graphs.

Vulnerability Measures of Transformation Graph Gxy+

2015 ◽  
Vol 26 (06) ◽  
pp. 667-675 ◽  
Author(s):  
Aysun Aytaç ◽  
Tufan Turaci
Keyword(s):  
Communication Networks ◽  
Network Topology ◽  
Interconnection Networks ◽  
Network Reliability ◽  
Network Robustness ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
System Robustness ◽  
The Cost ◽  
Cost Of Construction

Several factors have to be taken into account in the design of large interconnection networks. Optimal design is important both to achieve good performance and to reduce the cost of construction and maintenance. Practical communication networks are exposed to failures of network components. Failures between nodes and connections happen and it is desirable that a network is robust in the sense that a limited number of failures does not break down the whole system. Robustness of the network topology is a key aspect in the design of computer networks. A variety of measures have been proposed in the literature to quantify the robustness of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. In this paper, we study the vulnerability of interconnection networks to the failure of individual nodes, using a graph-theoretic concept of domination and strong-weak domination numbers of the transformation graph Gxy+ as a measure of network robustness.

Network robustness and residual closeness

2018 ◽  
Vol 52 (3) ◽  
pp. 839-847
Author(s):  
Aysun Aytaç ◽  
Zeynep Nihan Odabaş Berberler
Keyword(s):  
Complex Networks ◽  
Interconnection Networks ◽  
Network Reliability ◽  
Central Issue ◽  
Network Robustness ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
Individual Nodes

A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A variety of measures have been proposed in the literature to quantify the robustness of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. In this paper, we study the vulnerability of interconnection networks to the failure of individual nodes, using a graph-theoretic concept of residual closeness as a measure of network robustness which provides a much fuller characterization of the network.

scholarly journals Systems-level cancer gene identification from protein interaction network topology applied to melanogenesis-related functional genomics data

2009 ◽  
Vol 7 (44) ◽  
pp. 423-437 ◽  
Author(s):  
Tijana Milenković ◽  
Vesna Memišević ◽  
Anand K. Ganesan ◽  
Nataša Pržulj
Keyword(s):  
Protein Interaction ◽  
Network Topology ◽  
Interaction Network ◽  
Biological Processes ◽  
Cancer Gene ◽  
Cancer Genes ◽  
Clustering Methods ◽  
Ppi Network ◽  
Graph Theoretic ◽  
Ppi Networks

Many real-world phenomena have been described in terms of large networks. Networks have been invaluable models for the understanding of biological systems. Since proteins carry out most biological processes, we focus on analysing protein–protein interaction (PPI) networks. Proteins interact to perform a function. Thus, PPI networks reflect the interconnected nature of biological processes and analysing their structural properties could provide insights into biological function and disease. We have already demonstrated, by using a sensitive graph theoretic method for comparing topologies of node neighbourhoods called ‘graphlet degree signatures’, that proteins with similar surroundings in PPI networks tend to perform the same functions. Here, we explore whether the involvement of genes in cancer suggests the similarity of their topological ‘signatures’ as well. By applying a series of clustering methods to proteins' topological signature similarities, we demonstrate that the obtained clusters are significantly enriched with cancer genes. We apply this methodology to identify novel cancer gene candidates, validating 80 per cent of our predictions in the literature. We also validate predictions biologically by identifying cancer-related negative regulators of melanogenesis identified in our siRNA screen. This is encouraging, since we have done this solely from PPI network topology. We provide clear evidence that PPI network structure around cancer genes is different from the structure around non-cancer genes. Understanding the underlying principles of this phenomenon is an open question, with a potential for increasing our understanding of complex diseases.

scholarly journals Nakade — a graph theoretic concept in Go

2001 ◽  
Vol 235 (1-3) ◽  
pp. 385-397
Author(s):  
Tomoki Nakamigawa
Keyword(s):  
Graph Theoretic ◽  
Theoretic Concept

scholarly journals Robust cell tracking in epithelial tissues through identification of maximum common subgraphs

2016 ◽  
Author(s):  
Jochen Kursawe ◽  
Rémi Bardenet ◽  
Jeremiah J. Zartman ◽  
Ruth E. Baker ◽  
Alexander G. Fletcher
Keyword(s):  
Cell Tracking ◽  
Positional Information ◽  
Large Cell ◽  
Field Of View ◽  
Maximum Common Subgraph ◽  
Graph Theoretic ◽  
Epithelial Tissues ◽  
Theoretic Concept ◽  
Tissue Size ◽  
Epithelial Sheets

AbstractTracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Characterising cell growth, proliferation, intercalation and apoptosis in epithelia helps us to understand how morphogenetic processes such as tissue invagination and extension are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells entering or leaving the field of view between frames, cell neighbour exchanges, cell removals and cell divisions. However, current tracking methods for epithelial sheets are not robust to large morphogenetic deformations and require significant manual interventions. Here, we present a novel algorithm for epithelial cell tracking, exploiting the graph-theoretic concept of a ‘maximum common subgraph’ to track cells between frames of a video. Our algorithm does not require the adjustment of tissue-specific parameters, and scales in sub-quadratic time with tissue size. It does not rely on precise positional information, permitting large cell movements between frames and enabling tracking in datasets acquired at low temporal resolution due to experimental constraints such as photoxicity. To demonstrate the method, we perform tracking on the Drosophila embryonic epidermis and compare cell-cell rearrangements to previous studies in other tissues. Our implementation is open source and generally applicable to epithelial tissues.

Link-Centre and Indexes of a Kinematic Chain

1992 ◽  
Author(s):  
V. P. Agrawal ◽  
J. N. Yadav ◽  
C. R. Pratap
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Input Output ◽  
Function Generator ◽  
Kinematic Chains ◽  
Graph Theoretic ◽  
Optimum Selection ◽  
Theoretic Concept ◽  
Selection Of

Abstract A new graph theoretic concept of link-centre of a kinematic chain is introduced. The link-centre of a kinematic chain is defined as a subset of set of links of the kinematic chain using a hierarchy of criteria based on distance concept. A number of structural invariants are defined for a kinematic chain which may be used for identification and classification of kinematic chains and mechanisms. An algorithm is developed on the basis of the concept of distance and the link-centre for optimum selection of input, output and fixed links in a multi-degree-of-freedom function generator.

scholarly journals Cache Transition Systems for Graph Parsing

2018 ◽  
Vol 44 (1) ◽  
pp. 85-118 ◽  
Author(s):  
Daniel Gildea ◽  
Giorgio Satta ◽  
Xiaochang Peng
Keyword(s):  
Transition System ◽  
Tree Decomposition ◽  
Dependency Parsing ◽  
Semantic Parsing ◽  
Fixed Size ◽  
Transition Systems ◽  
Graph Theoretic ◽  
Theoretic Concept ◽  
The Relationship

Motivated by the task of semantic parsing, we describe a transition system that generalizes standard transition-based dependency parsing techniques to generate a graph rather than a tree. Our system includes a cache with fixed size m, and we characterize the relationship between the parameter m and the class of graphs that can be produced through the graph-theoretic concept of tree decomposition. We find empirically that small cache sizes cover a high percentage of sentences in existing semantic corpora.

PROTEIN STRUCTURE: INSIGHTS FROM GRAPH THEORY

2002 ◽  
Vol 01 (01) ◽  
pp. 187-211 ◽  
Author(s):  
SARASWATHI VISHVESHWARA ◽  
K. V. BRINDA ◽  
N. KANNAN
Keyword(s):  
Graph Theory ◽  
Protein Structure ◽  
Computer Networks ◽  
Electrical Engineering ◽  
Protein Structures ◽  
Large Body ◽  
Biological Information ◽  
Stability Function ◽  
Graph Theoretic ◽  
Efficient Extraction

The sequence and structure of a large body of proteins are becoming increasingly available. It is desirable to explore mathematical tools for efficient extraction of information from such sources. The principles of graph theory, which was earlier applied in fields such as electrical engineering and computer networks are now being adopted to investigate protein structure, folding, stability, function and dynamics. This review deals with a brief account of relevant graphs and graph theoretic concepts. The concepts of protein graph construction are discussed. The manner in which graphs are analyzed and parameters relevant to protein structure are extracted, are explained. The structural and biological information derived from protein structures using these methods is presented.

EPIDEMIOLOGY MODEL ON SHORTCUT AND SMALL WORLD NETWORKS

2009 ◽  
Vol 23 (10) ◽  
pp. 1249-1262 ◽  
Author(s):  
O. SHANKER ◽  
TAD HOGG
Keyword(s):  
Social Networks ◽  
Sensor Network ◽  
Computer Networks ◽  
Network Topology ◽  
Small World ◽  
Social Contagion ◽  
Small World Network ◽  
Small World Networks ◽  
Model Dependence ◽  
Human Animal

We show that the behavior of an epidemiology model depends sensitively on the shortcut density in the shortcut network. This is consistent with an earlier work on other processes on the shortcut network. We analytically study the reason for the sensitivity. The shortcut network is similar to the small world network, and it has the advantage that the model dependence on the shortcut density can be analytically studied. The model would be relevant to the spread of diseases in human, animal, plant or other populations, to the spread of viruses in computer networks, or to the spread of social contagion in social networks. It would also be relevant in understanding the variations in the load on routers connecting different computer networks, as the network topology gets extended by the addition of new links, and in analyzing the placement of certain special sensors in a sensor network laid out in a non-random way with some shortcut links.

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