Minimum Spanning Tree Research Articles

Rural Electrification of Selected Areas in the Northern Region of Ghana Viewed as a Minimum Spanning Tree Problem

Rural Electrification of Selected Areas in the Northern Region of Ghana Viewed as a Minimum Spanning Tree Problem

Minimum Spanning Tree‐Based Clustering for Chemical Evaluation of Commercial Nail Polish Samples Using Spectroanalytical Data

ABSTRACTThis study discusses potential toxic elements detection in conventional nail polish, including Cr and Pb. The noteworthy results highlight well‐established potential risks of elevated Cr and Pb concentrations. These elements are not allowed in the European Union. Implementing the minimum spanning tree (MST) approach and the isolation forest algorithm effectively clustered samples. Forty‐five samples were analyzed, and four clusters were identified. Two presented six samples with high concentrations of Fe (Cluster 1 with four samples) and Cr and Pb (Cluster 2 with two samples). The other 39 samples presented low concentrations of the determined elements (Co, Cr, Cu, Fe, Ni, and Pb). Cadmium, Zn, and Mn were not detected in any of the analyzed samples. Furthermore, integrating energy‐dispersive x‐ray fluorescence (ED‐XRF) and laser‐induced breakdown spectroscopy (LIBS) enabled fast direct analysis of nail polish samples, streamlining a swift and reliable data acquisition process. This research underscores the importance of ongoing vigilance and monitoring of potential health hazards associated with nail polish formulations, especially in regions with regulatory restrictions on certain elements.

Predicting the Conversion from Mild Cognitive Impairment to Alzheimer's Disease Using Graph Frequency Bands and Functional Connectivity-Based Features.

Accurate prediction of the progression from mild cognitive impairment (MCI) to Alzheimer's disease (AD) is crucial for disease management. Machine learning techniques have demonstrated success in classifying AD and MCI cases, particularly with the use of resting-state functional magnetic resonance imaging (rs-fMRI) data.This study utilized three years of rs-fMRI data from the ADNI, involving 142 patients with stable MCI (sMCI) and 136 with progressive MCI (pMCI). Graph signal processing was applied to filter rs-fMRI data into low, middle, and high frequency bands. Connectivity-based features were derived from both filtered and unfiltered data, resulting in a comprehensive set of 100 features, including global graph metrics, minimum spanning tree (MST) metrics, triadic interaction metrics, hub tendency metrics, and the number of links. Feature selection was enhanced using particle swarm optimization (PSO) and simulated annealing (SA). A support vector machine (SVM) with a radial basis function (RBF) kernel and a 10-fold cross-validation setup were employed for classification. The proposed approach demonstrated superior performance, achieving optimal accuracy with minimal feature utilization. When PSO selected five features, SVM exhibited accuracy, specificity, and sensitivity rates of 77%, 70%, and 83%, respectively. The identified features were as follows: (Mean of clustering coefficient, Mean of strength)/Radius/(Mean Eccentricity, and Modularity) from low/middle/high frequency bands of graph. The study highlights the efficacy of the proposed framework in identifying individuals at risk of AD development using a parsimonious feature set. This approach holds promise for advancing the precision of MCI to AD progression prediction, aiding in early diagnosis and intervention strategies.

Hopcroft’s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision Trees

We revisit Hopcroft’s problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O ( n 4/3 ) time, which matches the conjectured lower bound and improves the best previous time bound of \(n^{4/3}2^{O(\log ^*n)}\) obtained almost 30 years ago by Matoušek [ 58 ]. We describe two interesting and different ways to achieve the result: The first is randomized and uses a new two-dimensional version of fractional cascading for arrangements of lines; the second is deterministic and uses decision trees in a manner inspired by the sorting technique of Fredman [42]. The second approach extends to any constant dimension. Many consequences follow from these new ideas: For example, we obtain an O ( n 4/3 )-time algorithm for line segment intersection counting in the plane, O ( n 4/3 )-time randomized algorithms for distance selection in the plane and bichromatic closest pair and Euclidean minimum spanning tree in three or four dimensions, and a randomized data structure for halfplane range counting in the plane with O ( n 4/3 ) preprocessing time and space and \(O(n^{1/3})\) query time.

On Single-Objective Sub-Graph-Based Mutation for Solving the Bi-Objective Minimum Spanning Tree Problem.

We contribute to the efficient approximation of the Pareto-set for the classical NP-hard multiobjective minimum spanning tree problem (moMST) adopting evolutionary computation. More precisely, by building upon preliminary work, we analyze the neighborhood structure of Pareto-optimal spanning trees and design several highly biased sub-graph-based mutation operators founded on the gained insights. In a nutshell, these operators replace (un)connected sub-trees of candidate solutions with locally optimal sub-trees. The latter (biased) step is realized by applying Kruskal's single-objective MST algorithm to a weighted sum scalarization of a sub-graph. We prove runtime complexity results for the introduced operators and investigate the desirable Pareto-beneficial property. This property states that mutants cannot be dominated by their parent. Moreover, we perform an extensive experimental benchmark study to showcase the operator's practical suitability. Our results confirm that the sub-graph-based operators beat baseline algorithms from the literature even with severely restricted computational budget in terms of function evaluations on four different classes of complete graphs with different shapes of the Pareto-front.

Application of graph-curvature features in computer-aided diagnosis for histopathological image identification of gastric cancer

BackgroundHistopathology diagnosis is often regarded as the final diagnostic method for malignant tumors; however, it has some drawbacks. This study explored a computer-aided diagnostic method that can be used to identify benign and malignant gastric cancer using histopathological images. MethodsThe most suitable process was selected through multiple experiments by comparing multiple methods and features for classification. First, the U-net was applied to segment the image. Next, the nucleus was extracted from the segmented image, and the minimum spanning tree (MST) diagram structure that can capture the topological information was drawn. The third step was to extract the graph-curvature features of the histopathological image according to the MST image. Finally, by inputting the graph-curvature features into the classifier, the recognition results for benign or malignant cancer can be obtained. ResultsDuring the experiment, we used various methods for comparison. In the image segmentation stage, U-net, watershed algorithm, and Otsu threshold segmentation methods were used. We found that the U-net method, combined with multiple indicators, was the most suitable for segmentation of histopathological images. In the feature extraction stage, in addition to extracting graph-edge and graph-curvature features, several basic image features were extracted, including the red, green and blue feature, gray-level co-occurrence matrix feature, histogram of oriented gradient feature, and local binary pattern feature. In the classifier design stage, we experimented with various methods, such as support vector machine (SVM), random forest, artificial neural network, K nearest neighbors, VGG-16, and inception-V3. Through comparison and analysis, it was found that classification results with an accuracy of 98.57% can be obtained by inputting the graph-curvature feature into the SVM classifier. ConclusionThis study created a unique feature, the graph-curvature feature, based on the MST to represent and analyze histopathological images. This graph-based feature could be used to identify benign and malignant cells in histopathological images and assist pathologists in diagnosis.

Noise sensitivity of the minimum spanning tree of the complete graph

Abstract We study the noise sensitivity of the minimum spanning tree (MST) of the $n$ -vertex complete graph when edges are assigned independent random weights. It is known that when the graph distance is rescaled by $n^{1/3}$ and vertices are given a uniform measure, the MST converges in distribution in the Gromov–Hausdorff–Prokhorov (GHP) topology. We prove that if the weight of each edge is resampled independently with probability $\varepsilon \gg n^{-1/3}$ , then the pair of rescaled minimum spanning trees – before and after the noise – converges in distribution to independent random spaces. Conversely, if $\varepsilon \ll n^{-1/3}$ , the GHP distance between the rescaled trees goes to $0$ in probability. This implies the noise sensitivity and stability for every property of the MST that corresponds to a continuity set of the random limit. The noise threshold of $n^{-1/3}$ coincides with the critical window of the Erdős-Rényi random graphs. In fact, these results follow from an analog theorem we prove regarding the minimum spanning forest of critical random graphs.

The Integration of Dual Evaluation and Minimum Spanning Tree Clustering to Support Decision-Making in Territorial Spatial Planning

Spatial planning, a policy instrument for creating sustainable environments that meet the needs of the current and future generations, has been implemented extensively worldwide. However, it is difficult for urban planners to thoroughly determine the spatial value of a territory and make informed decisions regarding the efficient utilization of regional resources in the real world. This study proposes a novel methodological framework for spatial pattern optimization that can guide future land use by integrating Minimum Spanning Tree (MST) clustering with a comprehensive evaluation system (dual evaluation). Furthermore, the validity of this framework is demonstrated through a case study of territorial spatial planning in Deyang, China. The findings indicate that (1) the methodological framework presented in this study offers valuable guidance for the spatial arrangement of territorial resources, especially in practical projects; and (2) the combination of dual evaluation and MST clustering can facilitate automatic regionalization to identify spatial clusters exhibiting functional similarity in terms of land use. By focusing on methodological advancements, this study concludes that the integration of dual evaluation (DE) and MST clustering not only simplifies the identification of optimal land-use patterns but also promotes a more systematic and efficient approach to support spatial planning.

Minimum spanning tree analysis of EEG resting-state functional networks in schizophrenia

Schizophrenia is a serious and complex mental disease, known to be associated with various subtle structural and functional deviations in the brain. Recently, increased attention is given to the analysis of brain-wide, global mechanisms, strongly altering the communication of long-distance brain areas in schizophrenia. Data of 32 patients with schizophrenia and 28 matched healthy control subjects were analyzed. Two minutes long 64-channel EEG recordings were registered during resting, eyes closed condition. Average connectivity strength was estimated with Weighted Phase Lag Index (wPLI) in lower frequencies: delta and theta, and Amplitude Envelope Correlation with leakage correction (AEC-c) in higher frequencies: alpha, beta, lower gamma and higher gamma. To analyze functional network topology Minimum Spanning Tree (MST) algorithms were applied. Results show that patients have weaker functional connectivity in delta and alpha frequency bands. Concerning network differences, the result of lower diameter, higher leaf number, and also higher maximum degree and maximum betweenness centrality in patients suggest a star-like, and more random network topology in patients with schizophrenia. Our findings are in accordance with some previous findings based on resting-state EEG (and fMRI) data, suggesting that MST network structure in schizophrenia is biased towards a less optimal, more centralized organization.

Analysing Malaysian Technology Sector during COVID-19: A Minimum Spanning Tree Approach

This paper examines the structural changes of the companies listed in the technology sector in Bursa Malaysia during the COVID-19 pandemic. The closing price of each stock is used as the basis for calculating the cross-correlation between the companies' returns. Minimum spanning trees are employed to analyse the relationships and visualize the correlation changes for each period. Additionally, degree centrality is utilized to analyse the network's structure further. This study covers the period from 2020 to 2021 and involves 39 companies within the technology sector. The findings reveal significant fluctuations in the companies' correlations each year. Moreover, the most influential companies vary according to the period, demonstrating position changes. The fact that Inari Amertron (INAR), Revenue Group (REVE), and My EG Services (MYEG) consistently become leading players in different years shows how strong and influential they are in the technology sector. This suggests that these companies have the ability to shape market trends and possibly even control the direction of the industry. The results provide valuable insights for investors and policymakers, aiding in visualizing company relationships and facilitating strategic portfolio optimization.

An Amalgamated Kruskal’s Algorithm to ascertain the shortest route in the futuristic smart world

As the globe enters a new era, web applications will become indispensable to managing business. Businesses can easily grow, become simpler, and accomplish their objective much faster by employing web applications. Creating a web application in cloud computing allows for the more affordable leveraging of cloud-based services. This makes it easier to avoid setting up and maintaining several servers. To get around cloud computing’s built-in restrictions such as scalability, security, and bandwidth limitations, the future smart world of cloud computing will be coupled with LiFi connectivity. Beyond creating the web application, it is important to promote this web application among the network of users as quickly and effectively as possible. This manuscript proposes a strategy to address these challenges. There are two primary components to this MCDM technique. The first step is to model the problem as a graph and weigh the edges by employing the Hamacher aggregation operator. The second step involves using a fresh iteration of Kruskal’s technique in conjunction with this approach to discover a Minimum Spanning Tree as a resolution. This manuscript adds to the literature by solving real-world Minimum Spanning Tree problems by combining existing algorithms with MCDM techniques. This technique is demonstrated for marketing a web application(created via cloud service) in a future smart world using LiFi technology.

Characterization of Endothelial to Mesenchymal Transition in Air Pollution Mediated Atherosclerosis: Insights from Trajectory Inference and Functional Analyses in Single cell RNA Sequencing Data

Background: Air pollution is the world’s leading environmental risk factor for atherosclerotic cardiovascular disease (ASCVD). Regressive transcriptional reprogramming and transition of cells to primordial states has been identified as a driver of atherosclerosis. Endothelial cell to mesenchymal cell transition (EndoMT) whereby an endothelial cell transforms to a mesenchymal-like cellular phenotype is one such mechanism. However its relevance to air pollution exposure remains uncharacterized. Methods: Male ApoE−/− mice were inhalationally exposed to concentrated particulate matter <2.5μ component (PM2.5) or filtered air (FA, controls) using a Versatile Aerosol Concentration Enrichment System (VACES, 5–6 h/day, 5 d/week for 36 weeks, n = 7/group. PM2.5 concentrations were 70-80 μg/m3 or ~10X ambient levels. Following euthanasia, single-cell RNA-sequencing of aortic cells was performed using the 10-X platform (CA). For all subsequent analyses, aortic cell samples were integrated. Unsupervised clustering (k-NN) and low-dimensional space visualization (UMAP) were performed with a supervised graph method (Minimum Spanning Tree and Principal Curves) to infer and visualize trajectory analysis of novel cell lineages (branching and cell ordering in pseudotime/pseudospace). Functional analyses were carried out by statistical enrichment analysis using Over Representation Analysis (ORA) and Gene Set Enrichment Analysis (GSEA) against databases of Gene Ontologies (GO), Biological Pathways, putative regulatory motifs, proteins, or disease annotations to find over-representation of terms and functions. Pseudotime distribution assessed along exposure groups and cell-types lineages were statistically compared using GLM models. Differential Expression Analysis within lineages and between groups were tested by GLM and GAM models and FDR correction, followed by functional analyses. Results: Comparison of the pseudotime lineage with lineage root node at the endothelial cells revealed a similarity between observed endothelial (EC) to vascular smooth muscle (VSMC) cell transition with the differential transition noted with PM2.5 from FA. This overlap suggests a potential exaggeration of EC to VSMC transition in response to PM2.5 exposure. Differential gene expression profiling upon PM2.5-exposure in EC revealed significant changes in GO terms related to cell differentiation, cell migration, and regulation of cell population proliferation. Specific genes with variable patterns of expression (4481) were identified along the EC to VSMC lineage. KEGG pathway analysis along the lineage revealed enriched pathways including PI3K/Akt signaling pathway, MAPK signaling pathway, and Rap1 signaling pathway which are all implicated in the development and progression of atherosclerosis. Conclusion: Single-cell analysis reveals that chronic exposure to PM2.5 results in the exaggeration of EC to VSMC transition consistent with the EndoMT paradigm that may help explain the acceleration of ASCVD in response to air pollution exposure. Additional analysis of cell specific pathways may provide improved understanding of mechanisms progression of atherosclerosis in response to environmental exposures. NIH: 1R35ES031702-01, R01 HL155450, 3R35ES031702-02S1; Burroughs Wellcome Fund: 1060485. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Some Algorithms of Graph Theory in Cryptology

The inventive use of concepts from Graph Theory plays a significant role in hiding the original Plain-text for resulting in a significantly safe data transfer. In this work, the tree traversal algorithms like Inorder, Preorder, Postorder, Kruskal’s algorithm for making minimal spanning tree and the modified graph labelling scheme of graceful labelling allowing repetition of exactly one vertex label for certain graphs, have been employed to create highly hidden Cipher-texts. Encryption and decryption algorithms for all these methods are being presented in this work.

Transmission characteristics in Tuberculosis by WGS: nationwide cross-sectional surveillance in China

ABSTRACT China, with the third largest share of global tuberculosis cases, faces a substantial challenge in its healthcare system as a result of the high burden of multidrug-resistant and rifampicin-resistant tuberculosis (MDR/RR-TB). This study employs a genomic epidemiological approach to assess recent tuberculosis transmissions between individuals, identifying potential risk factors and discerning the role of transmitted resistant isolates in the emergence of drug-resistant tuberculosis in China. We conducted a population-based retrospective study on 5052 Mycobacterium tuberculosis (MTB) isolates from 70 surveillance sites using whole genome sequencing (WGS). Minimum spanning tree analysis identified resistance mutations, while epidemiological data analysis pinpointed transmission risk factors. Of the 5052 isolates, 23% (1160) formed 452 genomic clusters, with 85.6% (387) of the transmissions occurring within the same counties. Individuals with younger age, larger family size, new cases, smear positive, and MDR/RR were at higher odds for recent transmission, while higher education (university and above) and occupation as a non-physical workers emerged as protective factors. At least 61.4% (251/409) of MDR/RR-TB were likely a result of recent transmission of MDR/RR isolates, with previous treatment (crude OR = 2.77), smear-positive (cOR = 2.07) and larger family population (cOR = 1.13) established as risk factors. Our findings highlight that local transmission remains the predominant form of TB transmission in China. Correspondingly, drug-resistant tuberculosis is primarily driven by the transmission of resistant tuberculosis isolates. Targeted interventions for high-risk populations to interrupt transmission within the country will likely provide an opportunity to reduce the prevalence of both tuberculosis and drug-resistant tuberculosis.

Fuzzy Tree t -Spanners of Ratio Labelled Butterfly Network

Background/Objectives: The reliability and optimality of a communication system depend on the network that has a minimum distance. The minimum distance is the shortest path between the vertices. Even in error correction codes, the minimum Hamming distance ensures data integrity. Hence to have efficient routing protocols, the network is preferred to be a spanning tree that connects all the nodes of the communication system. As tree t- spanner is the optimization technique in determining minimum spanning tree, finding tree t-spanners of a ratio labelled fuzzy graph for the Butterfly network BF(n) is notion of this study. Methods: This study has introduced a new labelling called Ratio Labelling (RL) for examining the fuzziness in a crisp graph. Using the RL method, the crisp graphs were examined for the admittance of fuzziness and were thereby found, to have a tree t-spanners of ratio labelled fuzzy graphs. Findings: The quality of a network can be measured using the stretch factor of the network. The issues of network survival or link failures in a communication networks can be rectified by approximating the best flow spanner. As the optimal connectivity between the nodes is ensured by interconnection networks, the fuzzy tree t- spanners of undirected fuzzy Butterfly Network BF(n) are examined by labelling the vertices and edges using ratio labelling. The Breadth First Search (BFS) algorithm enhances the process of minimizing the spanning tree for an unweighted graph. Since the edge weightage is unique for all the edges of BF(n) under RL, searching for an edge with minimum weight by Kruskal’s algorithm or Prim’s algorithm are less meaningful. Hence, the BFS algorithm is adopted in finding the spanning tree T of Ratio Labelled BF(n). The bounds for the stretch factor t of a fuzzy tree t- spanner of ratio labelled BF(n) were obtained. Novelty: The literature survey shows that various classes of graphs were examined for the admissibility of tree t-spanners. Finding a tree t-spanner for a fuzzy graph was not found in literature, as per our knowledge. Extending the problem of finding a tree t -spanner of a ratio labelled fuzzy graph is an advancement in the field of fuzzy graphs. Keywords: Fuzzy Graph, Fuzzy distance, Ratio Labelling, Tree t- spanner, Butterfly Network

Voronoi diagrams and tree structures in HRP-EE: Enhancing IoT network lifespan with WSNs

Within the domain of the Internet of Things (IoT), wireless sensor networks (WSNs) play a pivotal role, facilitating advancements in sectors such as smart urban infrastructures, intelligent healthcare systems, and residential automation. Despite their versatility, WSNs grapple with challenges like limited energy reserves and constrained computational capacities, making energy conservation a paramount concern for IoT deployments underpinned by WSNs. This study introduces the Hybrid Routing Protocol for Efficient Energy (HRP-EE) designed to enhance the operational efficiency of WSNs. The HRP-EE protocol unfolds over three meticulous stages: the selection of cluster heads, the formation of clusters, and the establishment of routing pathways. Initially, the protocol evaluates nodes based on their residual energy and their Euclidean distance to the central sink (or gateway) device to designate apt cluster heads. Subsequently, these chosen cluster heads are integrated into the Voronoi diagram as central nodes to orchestrate cluster architectures. In the terminal stage, an innovative hybrid algorithm is instituted. This algorithm amalgamates the principles of the Minimum Spanning Tree for structuring intra-cluster communication trees and Dijkstra’s algorithm to ascertain the most efficient paths for inter-cluster data transmission from cluster heads to the sink device. The primary objective of this protocol is the judicious utilization of the sensor nodes’ energy, thereby optimizing the overall network longevity. To assess the proficiency of HRP-EE, we executed a series of simulations using NS2. Comparative analyses reveal that HRP-EE outperforms existing protocols such as LEACH-VA, PEGCP, and TBC, delivering superior energy efficiency, extended network lifespan, and enhanced throughput across both homogeneous and heterogeneous network architectures.

The concept of Minimal Spanning Tree (MST) for Symmetric Encryption

As the digital communication has become a vital part of the human life nowadays, cybercrimes are ever expanding. One major tool to protect the message from hacking and tampering is concealing the original information. Modern cryptography not only concerns the encryption of the message but also focuses on the protection of the encrypted information from cyber-attacks.Apart from secret communication modern cryptography focuses on authentication and integrity of the message. The present paper explains a symmetric block cipher basing on graph structures. In this technique the message is encrypted twice. The first stage encryption using adjacency matrix of undirected graph; the second stage using exclusive OR (XOR) operation on the output of first stage. Encryption/Decryption Keys are distinct for distinct blocks and distinct rounds; derived from Minimum Span Tree (MST) technique of an undirected graph. Here multiple peers can communicate messages simultaneously. One of the entries selects some random ASCII characters whose number is same as the block length and uploads those characters in the cloud. All the members of the group establish block keys using key generation technique which is secret among them.

Priority queues with decreasing keys

A priority queue stores a multiset of items, each item being a 〈key,value〉 pair, and supports the insertion of a new item and extraction of an item with minimum key. In applications like Dijkstra's single source shortest path algorithm and Prim-Jarník's minimum spanning tree algorithm, the key of an item can decrease over time. Usually this is handled by either using a priority queue supporting the deletion of an arbitrary item or a dedicated DecreaseKey operation, or by inserting the same item multiple times but with decreasing keys.In this paper we study what happens if the keys associated with the items in a priority queue can decrease over time without informing the priority queue, and how such a priority queue can be used in Dijkstra's algorithm. We show that binary heaps with bottom-up insertions fail to report items with unchanged keys in correct order, while binary heaps with top-down insertions report items with unchanged keys in correct order. Furthermore, we show that skew heaps, leftist heaps, and priority queues based on linking the roots of heap-ordered trees, like pairing heaps, binomial queues and Fibonacci heaps, work correctly with decreasing keys without any modifications. Finally, we show that the post-order heap by Harvey and Zatloukal, a variant of a binary heap with amortized constant time insertions and amortized logarithmic time deletions, works correctly with decreasing keys and is a strong contender for an implicit priority queue supporting decreasing keys in practice.

Graph analysis of functional brain networks under varying working memory load: An EEG-based minimum spanning tree approach

Conventional graph theory approach implemented in prior studies to understand brain topology during performance of cognitive tasks is biased and limits comparison of results across studies. This study employed minimum spanning tree (MST) analysis, an unbiased approach, to quantify changes in brain network organization under varying working memory (WM) load. We used 28-channel electroencephalography dataset of 26 subjects performing cognitive (0-, 2- and 3-back) tasks. We computed functional connectivity across channels using weighted phase lag index (wPLI) in multiple frequency bands and constructed MSTs of brain networks under varying WM conditions. Results reveal 0- back had significantly higher parietal alpha wPLI, lower frontal theta wPLI and lower central theta wPLI, than other conditions. In theta band, we observed more star-like topology in 0- back condition than 2- back or 3- back conditions. Our findings suggest sensitivity of these metrics to alterations in brain network topology under varying cognitive demand.

Low Functional network integrity in cognitively unimpaired and MCI subjects with depressive symptoms: results from a multi-center fMRI study

Evidence suggests that depressive symptomatology is a consequence of network dysfunction rather than lesion pathology. We studied whole-brain functional connectivity using a Minimum Spanning Tree as a graph-theoretical approach. Furthermore, we examined functional connectivity in the Default Mode Network, the Frontolimbic Network (FLN), the Salience Network, and the Cognitive Control Network. All 183 elderly subjects underwent a comprehensive neuropsychological evaluation and a 3 Tesla brain MRI scan. To assess the potential presence of depressive symptoms, the 13-item version of the Beck Depression Inventory (BDI) or the Geriatric Depression Scale (GDS) was utilized. Participants were assigned into three groups based on their cognitive status: amnestic mild cognitive impairment (MCI), non-amnestic MCI, and healthy controls. Regarding affective symptoms, subjects were categorized into depressed and non-depressed groups. An increased mean eccentricity and network diameter were found in patients with depressive symptoms relative to non-depressed ones, and both measures showed correlations with depressive symptom severity. In patients with depressive symptoms, a functional hypoconnectivity was detected between the Anterior Cingulate Cortex (ACC) and the right amygdala in the FLN, which impairment correlated with depressive symptom severity. While no structural difference was found in subjects with depressive symptoms, the volume of the hippocampus and the thickness of the precuneus and the entorhinal cortex were decreased in subjects with MCI, especially in amnestic MCI. The increase in eccentricity and diameter indicates a more path-like functional network configuration that may lead to an impaired functional integration in depression, a possible cause of depressive symptomatology in the elderly.