## What is/are Topological Analysis?

Topological Analysis - Some of these new methods are rooted in the topological analysis of the phase space of the underlying dynamics or on an appropriate reconstruction of it [1, 2] The state of a system can be described by its d state variables x1.^{[1]}Furthermore, a topological analysis was performed to screen the hub targets.

^{[2]}In this paper, the topological analysis is used to analyze the structure and size of flow separation in forward swept blades.

^{[3]}Topological analysis of 2 shows a trinodal (3,4,5) network with stoichiometry (3-c)2(4-c)(5-c)2 and a very rare topological type of 3,4,5L6.

^{[4]}In this paper, a different point of view towards urban planning is suggested concentrating on the topological analysis and relation between city elements.

^{[5]}A mixed-method was conducted including correlational and topological analysis of speech.

^{[6]}Using computer methods (ToposPro software package), a geometric and topological analysis of the crystal structure of the intermetallic Ce80Pd128In284-cF492 (a = 21.

^{[7]}The detector is based on a super-fine-grained nuclear emulsion, called a nano-imaging tracker (NIT), and it is capable of detecting neutron-induced proton recoils as tracks through topological analysis with sub-micrometric accuracy.

^{[8]}In this manuscript, we describe the DELTA Science Gateway, which integrates several types of mathematical and topological analysis software for chemical data analysis.

^{[9]}0, and the core targets were obtained by topological analysis.

^{[10]}Using computer methods (ToposPro software package), the geometric and topological analysis is carried out of the crystal structure of the intermetallic compound Ta156Al288-cF444 (a = 19.

^{[11]}Topological analysis of ZSTU-10 reveals two interpenetrated 3,6-connected nets with an rtl (rutile) topology.

^{[12]}A topological analysis of the calculated electron density, was performed both for periodic and molecular models of Ag2X (X = S, Se).

^{[13]}STRING database and Cytoscape’s topological analysis revealed 80 potential targets related to the antidepressant mechanism of ZZHPD.

^{[14]}Topological analysis determined the key genes with the highest centroid and their expressions were further verified using public datasets and quantitative real-time polymerase chain reaction.

^{[15]}Topological analysis of the electron density in Al3Ti alloys revealed two interesting types of interactions between the atoms in the layered Al3Ti alloy structure lattice; viz.

^{[16]}Furthermore, a topological analysis of the electron density using QTAIM, ELF and DORI tools was performed.

^{[17]}The topological analysis showed that in most of the rhombencephalon the gray matter is arranged in four longitudinal zones or areas, termed area ventralis, area intermedioventralis, area intermediodorsalis and area dorsalis.

^{[18]}The topological analysis of complex 1 showed that the underlying net is characterized by an unknown topological type and point symbol {342.

^{[19]}Potential energy surface analysis of the Sc-ion reaction with water molecules, topological analysis of bonds, and the effect of sequential solvation up to 6 water molecules have been examined.

^{[20]}In particular, topological analysis shows, at the global scale and in the 0.

^{[21]}However, topological analysis of net relations revealed that no transformations can be applied to convert H-bonded networks in the experimental unit cells, and DSC data indicate no solid-state reactions at heating.

^{[22]}The core targets of YBD for the treatment of asthma were screened according to topological analysis based on degree parameters.

^{[23]}The topological analysis revealed that the 4,8-connected net of WSU-30 contains the underlying topology, alb-4,8-P21/c-1, while the mixed linker WSU-31 possesses a 3,10-connected net known as 3,10T31 topology.

^{[24]}Topological analysis identified additional gene signatures that differentiated patients with COVID-19 from patients with influenza, including insulin resistance, mitochondrial oxidative stress and interferon signalling.

^{[25]}70 Å) supported by topological analysis of electron density.

^{[26]}The conformational analysis, thermochemical analysis, frequency analysis, and topological analysis were conducted to determine the interactions of hydrogen-bonded molecular clusters.

^{[27]}The topological analysis indicated that the crystal structure displays a topology TCF-x.

^{[28]}Furthermore, the topological analysis of the charge density of intermolecular interactions was described.

^{[29]}Interaction network construction and topological analysis yielded 60 hub targets, of which 18 were major hub targets, among which IL-6, IL-8, TNF, PI3K, MAPK, and NF-κB (RELA) are the most important in LYT's treatment of AAD-induced MetS.

^{[30]}A chemoreactom analysis of CDP-choline, betahistine, ethyl-methyl-hydroxypyridine succinate (EMHPS), vinpocetine, and nicergoline was conducted using the computational methods of the theory of topological analysis of chemographs.

^{[31]}Different function units were defined by topological analysis of TME.

^{[32]}For the first time, the frontier molecular orbital (FMO) analysis, orbital-weighted dual descriptor (OW DD) analysis and Atoms-In-Molecules (AIM) topological analysis were combined to study the degradation path of RhB from the atomic point of view.

^{[33]}Topological analysis of SARS-CoV-2 E protein has shown that the N-terminus is localized within intracellular organelles, whereas the C-terminus is localized in the cytoplasm.

^{[34]}Here, we apply a combined technique of HR-TEM characterization, topological analysis, and atomistic simulations to explore the facets that bound the { 11 2 ¯ 2 } 11 23 ¯ > twin in Ti.

^{[35]}Topological analysis and community detection in mobility complex networks have an essential role in many contexts, from economics to the environmental agenda.

^{[36]}Furthermore, the topological analysis of the electron density has been performed for all investigated minerals.

^{[37]}The underlying topology of the CPs was illustrated by the topological analysis of the H-bonded structure of CP 1, which revealed a 3,4,6-connected trinodal net.

^{[38]}Therefore, the need for fracture network characterization based on topological analysis has recently emerged.

^{[39]}This article introduces progressive algorithms for the topological analysis of scalar data.

^{[40]}Current research is focused on volumetric analyses, while topological analysis of ventricular surfaces remains understudied.

^{[41]}Results According to topological analysis results, AKT1, MAPK1, ESR1, and SRC are critical genes for RRP to treat osteoporosis, and they have high binding activity with stigmasterol and sitosterol.

^{[42]}Moreover, core genes were identified by topological analysis of protein–protein interaction (PPI) network and gene–phenotype correlation analysis.

^{[43]}Here, we combine experiments, simulations, and topological analysis to identify universal mechanical interaction properties that determine early-stage biofilm architectures of different bacterial species.

^{[44]}The nature of imprinting was obtained by the topological analysis of electron density of stable complexes of NOR and TFMAA based on the atom in molecule theory.

^{[45]}For the first time, the Fukui index (f−), the highest occupied molecular orbital (HOMO), and atoms-in-molecules (AIM) topological analysis were used to analyze the active sites and covalent bonds of IBF molecules that were susceptible to the attack of ROS during photocatalysis, and the results were in good agreement with the LC-MS/MS intermediate detection.

^{[46]}Topological analysis of the electron distribution unambiguously describe H2O ⋯ Na+ ionic interactions.

^{[47]}Based on topological analysis of this interaction network, we obtained information on degree, clustering coefficient, connected components, and centrality of these interactions.

^{[48]}In contrast to wavefunction-based analyses, topological analysis of the electron density affords the advantage of analyzing a physical observable: the electron density.

^{[49]}Structural and topological analysis of its atomic structure reveals a high number of predominantly icosahedral densely packed Zn-centred clusters.

^{[50]}

## electron localization function

Topological analysis, namely electron localization function (ELF) and localized orbital locator (LOL) maps reveals that the interaction is non-covalent.^{[1]}Theoretical topological analysis of the electron density, according to the Quantum Theory of Atoms in Molecule (AIM), electron localization function (ELF) and the localized orbital locator (LOL) have been performed.

^{[2]}The topological analysis was carried out on the basis of theories of Atoms in Molecules (AIM—molecular topology, properties of critical points, AIM charges) and Electron Localization Function (ELF—2D maps showing bonding patterns, calculation of electron populations in the hydrogen bonds).

^{[3]}Topological analysis of the atoms in molecules (AIM), electron localization function (ELF), Mayer bond index and local aromaticity analysis were applied to study the theoretical and electronic structure of the presented molten salts molecules, and the nature of C-N, N-H, N-S, O-H, and H-Cl bonding was investigated.

^{[4]}Electron localization function (ELF) topological analysis of the bonding changes along the I-DA reactions shows that they are very similar to those in polar DA reactions.

^{[5]}The electron rearrangements along the preferred pathways of these 32CA reactions were studied using the topological analysis of the electron localization function (ELF).

^{[6]}The electron reorganization along the most preferred pathway of the [2+4] cycloaddition reaction between 2-phenylsulfonyl-1,3-butadienes and cyclopentadiene have been studied using the topological analysis of the electron localization function (ELF).

^{[7]}Topological analysis of the electron localization function at the B3LYP/6-311++G (2d,d,p) level of theory indicate that the catastrophe sequence 1-6-C†TSC†F C†C-0 begins with the N4-N5 bond breaking, elimination of nitrogen molecule and increasing of non-bonding monosynaptic attractor on N4 atom, and then changing of topological signature of C2-N4 bond, breaking of C1-C2 bond, and formation of pseudo-radical centers on C1 and C2 atoms.

^{[8]}The M–O bonds were characterized based on Atoms– in–molecules (AIM) and Electron Localization Function (ELF) in the topological analysis.

^{[9]}Topological analysis of the electron localization function (ELF) was applied to study the nature of the molecule-surface interactions.

^{[10]}Both electron localization function and AIM topological analysis reveal that the step associated with the attack of the 3Σ-g-O2 molecule on the intermediate 3MC characterizes the formation of the only new O2-C3 single bond, which occurs in a stepwise mechanism, in contrast to the Δg-O2 reaction with 15 species.

^{[11]}The topological analysis of the electron localization function (ELF) and localized orbital locator (LOL) revealed that the charge localization around hydrogen atoms.

^{[12]}In an attempt to clarify these points, we have investigated five 22-CPs and their corresponding toluene dimers by molecular orbitals analysis, electron density difference analysis, some topological analysis of ρ (quantum theory of atoms in molecules (QTAIM), electron localization function (ELF) and noncovalent interactions (NCI)), and energy decomposition analysis with natural orbitals for chemical valence (EDA-NOCV).

^{[13]}Topological analysis of the electron localization function (ELF) of dieniminiums showed that their electronic structures can been seen as the sum of those of butadiene and ethaniminium.

^{[14]}Topological analysis of electron localization function and electron density at the B3LYP/6-311G(d,p) level reveal that the reaction can be occurred as going through seven turning points defined as methyl benzoylformate 8-CF†FF†TSFC†[CF†]-0: methyl benzoate + carbon monoxide.

^{[15]}The topological analysis of the Electron Localization Function (ELF) confirms 3D character of (Fe2Ge2) layers similar to reported 122 iron tetrelides YFe2Ge2 and CaFe2Si2.

^{[16]}

## protein protein interaction

The STRING database was used for protein-protein interaction (PPI) network construction and topological analysis, while DAVID was used for Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analyses of the core targets.^{[1]}The protein-protein interaction (PPI) network was then generated by the Sting database and subjected to Cytoscape software to harvest major and core targets network by topological analysis.

^{[2]}Computational analysis of protein-protein interactions can be carried out in various ways, including topological analysis and clustering of protein-protein interaction networks.

^{[3]}Then, gene enrichment analysis, protein-protein interaction (PPI) network, miRNA-hub gene regulatory network and TF-hub gene regulatory network construction, and topological analysis were performed on the DEGs by the Gene Ontology (GO), REACTOME pathway, STRING, HiPPIE, miRNet, NetworkAnalyst and Cytoscape.

^{[4]}The hub-genes were screened by building protein-protein interaction sub-networks with 12 topological analysis methods.

^{[5]}RESULT CXCL10, CMPK2, RSAD2, SERPINA3, TNFAIP6, CXCL14, IVNS1AB, and ZMAT3 were selected based on the enrichment and topological analysis of the constructed protein-protein interaction (PPI) network.

^{[6]}Then, the protein-protein interactions (PPIs) of DEGs were performed by STRING database, the result was integrated and visualized via applying Cytoscape software, and the hub genes in this PPI network were selected by MCODE and topological analysis.

^{[7]}Generation of a protein-protein interaction network facilitated the selection of connected nodes for the construction of a shared disease- and drug-target interaction network model, and topological analysis identified the most highly connected nodes.

^{[8]}After that we also constructed protein-protein interaction network (PPI) considering the differentially expressed genes (DEGs) of CHKIV and identified hub genes based on topological analysis.

^{[9]}The protein-protein interactions (PPI) network of DEGs was constructed by STRING V11 database, and 11 hub genes were selected through intersection of 11 topological analysis methods of CytoHubba in Cytoscape plug-in.

^{[10]}After the production of putative therapeutic targets for dominant diseases and harmful targets of adverse reactions (ADRs) induced by THH, the protein-protein interactions (PPIs), topological analysis and pathway enrichment were established to distinguish the hub targets and pathways.

^{[11]}Then, Gene Ontology (GO) and pathway enrichment analysis, protein-protein interaction (PPI) network, modules, miRNA-hub gene regulatory network construction and TF-hub gene regulatory network construction, and topological analysis were performed.

^{[12]}The present study aimed to screen hub genes by constructing protein-protein interaction (PPI) subnetworks using topological analysis methods, as well as reveal their clinical significance through big data analytics and their association with the clinicopathological features.

^{[13]}Methods First, we found common targets of astragalus membranaceus and disease, protein-protein interaction (PPI) network was built by String, and then key targets were screened from these common targets by topological analysis.

^{[14]}

## density functional theory

Short supramolecular Br···Br and I···I contacts in chalcogenides Ti4Se9I6, V4S9Br4, Ta4S9Br8, and Ta4Se9I8 with a square {M4Q9} core are theoretically studied by quantum chemical calculations within the density functional theory (ωB97XD/DZP-DKH) and the QTAIM topological analysis of the electron density distribution.^{[1]}Furthermore, density functional theory (DFT) simulation performed at the B3PW91 level of theory as well as a topological analysis were introduced to elucidate theoretically the interfacial interaction at the molecular-scale associated with OTC sorption on both adsorbents.

^{[2]}In this work we describe the ion conductivity in the selected structures in detail by using of a set of methods: analysis of free space in crystals (geometrical-topological analysis, based on the Voronoi partitioning approach), calculation of the Zn2+-ion migration energy barrier within the bond valence site energy method, and calculation of the Zn2+-ion energy barriers within the density functional theory approach.

^{[3]}The structural data from X-ray diffraction are linked to calculated conformational energies from density functional theory (DFT) and topological analysis results obtained from quantum theory of atoms in molecules (QTAIM) calculations.

^{[4]}To untangle such properties, both density functional theory calculation and topological analysis were used.

^{[5]}We present in this work the density functional theory (DFT) calculations of the electronic structure, topological analysis and spectroscopic properties on sandwich indenyl complexes of ruthenium (ŋ5-C9H7) RuL with L= (ŋ5-C9H7) 1 and (ŋ5-C5H5) 2 in the gas phase and in THF, CH2Cl2, MeCN solvents.

^{[6]}To explain the sensing mechanisms and difference in adsorption behavior of Pb2+ and Cd2+ ions on EG in water-based solutions, we performed van-der-Waals (vdW)-corrected density functional theory (DFT) calculations and non-covalent interaction (NCI) analysis, extended charge decomposition analysis (ECDA), and topological analysis.

^{[7]}

## bond critical point

Topological analysis of the electron density identifies no bond critical point (BCP) between the two sp2 hybridized silicon atoms.^{[1]}Quantum topological analysis using Bader's Atoms in Molecules (AIM) theory revealed bond paths and bond critical points (BCP) in these structures suggesting its nature and energetics to be similar to weak hydrogen bonding.

^{[2]}Topological analysis employing QTAIM shows that most of the charge density and the Laplacian values at bond critical points (BCPs) of the hydrogen bonds of the MSA···(H2SO4)n (n = 1-3) complexes fall within the standard hydrogen-bond criteria.

^{[3]}General feature of these complexes is their ability to form halogen bonding (XB) in solid state; the energies of XBs were estimated based on the QTAIM analysis results (DFT calculations were used to get electron density, and then the topological analysis was used to estimate the energies via empirical correlations between the interaction energy and the potential or kinetic energy density of electrons at the bond critical points (3, –1)).

^{[4]}The Bader topological analysis of the electron density at the bond critical point shows that the closed-shell interaction of the Mn–O3 and Mn–O4 bonds in both materials increases with increasing Ueff, which justifies the decrease of Jnn with increasing Ueff.

^{[5]}The topological analysis of the electron density of metronidazole was performed using Bader's quantum theory of atoms in molecules to determine the electron density and the Laplacian of the electron density at the bond critical point of the molecule.

^{[6]}

## electron density distribution

The nature and energies of intermolecular noncovalent interactions, which are responsible for the supramolecular dimerization, are studied theoretically using DFT calculations, and the topological analysis of the electron density distribution is performed within the formalism of Bader's theory (QTAIM method).^{[1]}In addition, by employing a novel topological analysis of procrystal electron density distribution as applied to interfacial solid-state ionics, we thoroughly assess Li-ion conductivity through the investigated interfaces.

^{[2]}The nature and energies of intermolecular noncovalent interactions, which are responsible for the supramolecular dimerization, are studied theoretically using DFT calculations, and the topological analysis of the electron density distribution is performed within the formalism of Bader′s theory (QTAIM method).

^{[3]}Rare Type II F···F interactions were studied by DFT calculations and topological analysis of the electron density distribution within the formalism of Bader’s theory (QTAIM method).

^{[4]}A topological analysis of the electron density distribution (EDD) revealed little difference between the two polymorph internal systems.

^{[5]}Non-covalent chlorine···chlorine interactions were detected for 5 in the solid state and studied by DFT calculations and topological analysis of the electron density distribution within the framework of Bader’s theory (QTAIM method).

^{[6]}

## bonding changes along

ELF topological analysis of the bonding changes along the reaction establishes its non-concerted two-stage one-step mechanism, in which the nucleophilic attack of the carbenoid carbon of DFAY on the electrophilic carbonyl carbon of the ynal characterizes the cb-type reactivity of this three-atom component (TAC).^{[1]}The electron reorganization along the uncatalyzed one-step mechanism has been investigated by the ELF topological analysis of the bonding changes along with the CA reaction.

^{[2]}ELF topological analysis of the bonding changes along the I-DA reactions shows that they are very similar to those in polar DA reactions.

^{[3]}

## protein interaction network

Topological analysis of these networks reveals that solute carrier family 2 (glucose transporter) member 4 (SLC2A4) and tubulin β-2C (TUBB2C) are centrally located in the protein interaction network.^{[1]}The predicted small molecules were prioritized on the basis of topological analysis of the chemical-protein interaction network, which was inferred by integrating the drug-target network, NiV-human interaction network, and human protein-protein interaction network.

^{[2]}

## Network Topological Analysis

Additionally, the protein–protein interaction network analysis was used to identify the potential 20 hub messenger RNAs (mRNAs) while the network topological analysis was used to identify nine candidate long non-coding RNAs (lncRNAs).^{[1]}Furthermore, the analysis of metabolomics, together with network topological analysis in different phases of silicosis, revealed that urine myristic acid, serum 4-hydroxyproline, and L-arginine could be regarded as diagnosis biomarkers in the early phase and formation of pulmonary fibrosis in the latter phases of silicosis.

^{[2]}Pharmacological network topological analysis, molecular docking, bacterial adhesion, and invasion pathway verification assays were performed to identify the other molecular mechanisms of Pingwei Pill as a colistin potentiator against Gram-negative bacteria infection.

^{[3]}Moreover, 7 core targets (PIK3CA, AKT1, SRC, MAPK8, MAPK14, ERBB2 and CCND1) resulted from the intersection of KEGG and PPI network topological analysis were used to dock with imperatorin, which indicated that imperatorin could preferably fit in the binding pocket of the above target proteins, except for CCND1.

^{[4]}Network topological analysis, applied to plant proteomes profiled in different single or combined nutritional conditions, can therefore assist in identifying novel players involved in multiple homeostatic interactions.

^{[5]}MetaboAnalyst database was used in metabolic pathway analysis and the network topological analysis.

^{[6]}Furthermore, a “SZF-key targets-DKD” network topological analysis showed that active ingredients like M51, M21, M5, M71, and M28 and targets like EGFR, MMP9, MAPK8, PIK3CA, and STAT3 might play important roles in the process of SZF treating in DKD.

^{[7]}Moreover, the 63 key targets were screened by the intersection of the targets above, and by network topological analysis.

^{[8]}This model has sometimes been supplemented with network topological analysis.

^{[9]}A total of 188 shared targets were identified by network topological analysis, which were closely associated to the anti-VD effects of SZJNF.

^{[10]}We integrated the idea of wavelet and network topological analysis to provide a novel way to detect non-random species associations across scales and along gradients using continuous or presence-absence ecological data.

^{[11]}Subsequently, we perform network topological analysis and gene set enrichment analysis.

^{[12]}

## Elf Topological Analysis

The original two-component dative zinc-amido bond is unravelled by ELF topological analysis.^{[1]}ELF topological analysis of the bonding changes along the reaction establishes its non-concerted two-stage one-step mechanism, in which the nucleophilic attack of the carbenoid carbon of DFAY on the electrophilic carbonyl carbon of the ynal characterizes the cb-type reactivity of this three-atom component (TAC).

^{[2]}The electron reorganization along the uncatalyzed one-step mechanism has been investigated by the ELF topological analysis of the bonding changes along with the CA reaction.

^{[3]}ELF topological analysis of dieniminiums shows that its electronic structure can been seen as the sum of those of butadiene and ethaniminium.

^{[4]}ELF topological analysis of the bonding changes along the I-DA reactions shows that they are very similar to those in polar DA reactions.

^{[5]}ELF topological analysis of the bond formation along the IM32CA reaction indicates that in spite of the high activation energy associated to this intramolecular reaction, it shows a pmr-type mechanism characterised by the presence of a pseudoradical carbon at the phenyldiazomethane framework.

^{[6]}

## Vium Topological Analysis

Core metabolites that played an important role in the DCM networks were identified via topological analysis.^{[1]}PPI networks of the genes were constructed using STRING, and the core targets were screened via topological analysis.

^{[2]}Feature genes in the miRNA-mRNA network were identified via topological analysis and a recursive feature elimination algorithm.

^{[3]}

## My Topological Analysis

Our topological analysis identified an integrated disease-phase specific glial landscape that is shared across neurodegenerative conditions affecting the central nervous system.^{[1]}Our topological analysis of the chemical pressure (CP) scalar field, easily derived from these standard first-principles electronic computations, reveals that CP minima appear just at the precise positions of the nonmetallic elements in typical inorganic crystals presenting the above metallic subarrays: CaF2, rock-salt and CsCl-type phases of CaX (X = O, S, Se, Te), BaSnO3, K2S, and NaX (X = F, Cl, Br, I).

^{[2]}

## Aim Topological Analysis

AIM topological analysis revealed that a closed shell electrostatic interaction is dominant.^{[1]}Both electron localization function and AIM topological analysis reveal that the step associated with the attack of the 3Σ-g-O2 molecule on the intermediate 3MC characterizes the formation of the only new O2-C3 single bond, which occurs in a stepwise mechanism, in contrast to the Δg-O2 reaction with 15 species.

^{[2]}

## Through Topological Analysis

Through topological analysis and probability analysis, we investigate the characterization of delay propagation among airports and the impact of different types of airports on delay propagation.^{[1]}Through topological analysis of the reconstructed 3D magnetic field, it is found that the MFR begins to form early on 2014 January 6; then with its magnetic twist degree continuously increasing for over 30 hr, it becomes highly twisted with field lines winding numbers approaching six turns, which might be the highest twisting degree in extrapolated MFRs that have been reported in the literature.

^{[2]}

## Performed Topological Analysis

For this purpose, as a case study, we have performed topological analysis of 2391 global genomic sequences of SARS-CoV-2 in association with SARS-CoV-1 and MERS-CoV using an integrated semi-alignment based computational technique.^{[1]}To mine for novel prognostic signatures associated with GC, we performed topological analysis, a random walk with restart algorithm, in the GCsLMM from three levels, miRNA-, mRNA-, and lncRNA-levels.

^{[2]}

## Qtaim Topological Analysis

Short supramolecular Br···Br and I···I contacts in chalcogenides Ti4Se9I6, V4S9Br4, Ta4S9Br8, and Ta4Se9I8 with a square {M4Q9} core are theoretically studied by quantum chemical calculations within the density functional theory (ωB97XD/DZP-DKH) and the QTAIM topological analysis of the electron density distribution.^{[1]}QTAIM topological analysis suggests the presence of predominantly electrostatic interaction between the interacting monomers.

^{[2]}

## Combinatorial Topological Analysis

The combinatorial topological analysis and modeling of self-assembly of the K 78 In 160 - hP 238 (space group P -3 m 1, a = b = 17.^{[1]}A combinatorial topological analysis and modeling of the self-assembly of crystal structures of LiCaSn-hP9 (space group P3m1, V = 230.

^{[2]}

## topological analysis revealed

AIM topological analysis revealed that a closed shell electrostatic interaction is dominant.^{[1]}STRING database and Cytoscape’s topological analysis revealed 80 potential targets related to the antidepressant mechanism of ZZHPD.

^{[2]}The topological analysis revealed that the 4,8-connected net of WSU-30 contains the underlying topology, alb-4,8-P21/c-1, while the mixed linker WSU-31 possesses a 3,10-connected net known as 3,10T31 topology.

^{[3]}Topological analysis revealed that, compared with HCs, CD-HCU group were characterized by decreased small-worldness (σ), decreased global efficiency, and increased path length (λ).

^{[4]}The topological analysis revealed that the topology of CUST-551 is based on 3-8-connected net with the point symbol {43·624·8}{43}2, but CUST-552 is 3-10-connected with the point symbol {43}2{48·66·827·124}{4}2.

^{[5]}Topological analysis revealed 14 key gene targets such as MAPK8, MAPK14, EGFR and PTGS2.

^{[6]}Topological analysis revealed binodal nets with the flu and tcj/hc topology in 1 and 2, respectively.

^{[7]}Topological analysis revealed that NEAT1 was a hub lncRNA for the early response subtype, and its ceRNAs could predict patient survival.

^{[8]}Topological analysis revealed that both the number and strength of hydrogen bonds were greater for the OH−(H2O)4 cluster compared with the OH+(H2O)4 and OH(H2O)4 clusters.

^{[9]}

## topological analysis method

The hub-genes were screened by building protein-protein interaction sub-networks with 12 topological analysis methods.^{[1]}From a protein–protein interaction (PPI) network established by the STRING database, Cytoscape software identified hub genes with the two topological analysis methods maximal clique centrality and Degree algorithm to construct a miRNA-hub gene network.

^{[2]}Time series clustering was performed using topological analysis methods.

^{[3]}The topological analysis method is used to determine the formation and evolution of the vortices and to better understand the mechanism of the heat transfer enhancement.

^{[4]}The protein-protein interactions (PPI) network of DEGs was constructed by STRING V11 database, and 11 hub genes were selected through intersection of 11 topological analysis methods of CytoHubba in Cytoscape plug-in.

^{[5]}The present study aimed to screen hub genes by constructing protein-protein interaction (PPI) subnetworks using topological analysis methods, as well as reveal their clinical significance through big data analytics and their association with the clinicopathological features.

^{[6]}

## topological analysis identified

Topological analysis identified additional gene signatures that differentiated patients with COVID-19 from patients with influenza, including insulin resistance, mitochondrial oxidative stress and interferon signalling.^{[1]}Our topological analysis identified an integrated disease-phase specific glial landscape that is shared across neurodegenerative conditions affecting the central nervous system.

^{[2]}Generation of a protein-protein interaction network facilitated the selection of connected nodes for the construction of a shared disease- and drug-target interaction network model, and topological analysis identified the most highly connected nodes.

^{[3]}The topological analysis identified the XB as a directional but weak σ hole interaction and revealed secondary contacts between peripheral regions of opposite charge.

^{[4]}Topological analysis identified several critical hypoxiamiRs and network perturbations confirmed their importance in the network.

^{[5]}

## topological analysis result

Results According to topological analysis results, AKT1, MAPK1, ESR1, and SRC are critical genes for RRP to treat osteoporosis, and they have high binding activity with stigmasterol and sitosterol.^{[1]}Results: According to topological analysis results, AKT1, MAPK1, ESR1, SRC, and MMP9 are key genes for RRP to treat osteoporosis, and they have high binding activity with stigmasterol and sitosterol.

^{[2]}The structural data from X-ray diffraction are linked to calculated conformational energies from density functional theory (DFT) and topological analysis results obtained from quantum theory of atoms in molecules (QTAIM) calculations.

^{[3]}Topological analysis results are in accordance with the complex network representation of biological processes.

^{[4]}

## topological analysis reveal

Topological analysis reveals that the two structures are polytypes.^{[1]}Both electron localization function and AIM topological analysis reveal that the step associated with the attack of the 3Σ-g-O2 molecule on the intermediate 3MC characterizes the formation of the only new O2-C3 single bond, which occurs in a stepwise mechanism, in contrast to the Δg-O2 reaction with 15 species.

^{[2]}The topological analysis reveals the complexity and core–periphery structure of the inter-provincial trade network.

^{[3]}Atoms in molecules topological analysis reveals that the Laplacian of the charge density of the bimolecular interactions in the GA/OA/PA-MHS/MSA/HMSA complexes is higher than the upper value of the hydrogen bond criteria.

^{[4]}

## topological analysis showed

The topological analysis showed that in most of the rhombencephalon the gray matter is arranged in four longitudinal zones or areas, termed area ventralis, area intermedioventralis, area intermediodorsalis and area dorsalis.^{[1]}Furthermore, a “SZF-key targets-DKD” network topological analysis showed that active ingredients like M51, M21, M5, M71, and M28 and targets like EGFR, MMP9, MAPK8, PIK3CA, and STAT3 might play important roles in the process of SZF treating in DKD.

^{[2]}The topological analysis showed that compounds 1 and 2 present novel topology for net: 1.

^{[3]}

## topological analysis show

In particular, topological analysis shows, at the global scale and in the 0.^{[1]}Topological analysis shows that JXUST-5 could be simplified as an uninodal fes topology with a point symbol of {4.

^{[2]}Topological analysis shows that Zn-MOF exhibits a utp uninodal 3-connected 3D 2-interpenetrating framework with the point symbol (103).

^{[3]}

## topological analysis indicated

The topological analysis indicated that the crystal structure displays a topology TCF-x.^{[1]}Topological analysis indicated a non-trivial bond critical and ring critical point involving two non-covalently bonded fluorine atoms in perfluorinated quinoline, 1,8-naphthyridine and 1,10-phenathroline.

^{[2]}The PPI network and topological analysis indicated that IL-6, MAPK8, MMP-9, TNF, and MAPK1 shared the highest centrality among all.

^{[3]}