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Graph theory in higher order topological analysis of urban scenes

Almeida, J. -P. de; Morley, J. G.; Dowman, I. J.
Fonte: Universidade de Coimbra Publicador: Universidade de Coimbra
Tipo: Artigo de Revista Científica Formato: aplication/PDF
ENG
Relevância na Pesquisa
66.08%
Interpretation and analysis of spatial phenomena is a highly time-consuming and laborious task in several fields of the Geomatics world. That is why the automation of these tasks is especially needed in areas such as GISc. Carrying out those tasks in the context of an urban scene is particularly challenging given the complex spatial pattern of its elements. The aim of retrieving structured information from an initial unstructured data set translated into more meaningful homogeneous regions can be achieved by identifying meaningful structures within the initial collection of objects, and by understanding their topological relationships and spatial arrangement. This task is being accomplished by applying graph theory and by performing urban scene topology analysis. For this purpose, a graph-based system is being developed, and LiDAR data are currently being used as an example scenario. A particular emphasis is being given to the visualisation aspects of graph analysis, as visual inspections can often reveal patterns not discernable by current automated analysis techniques. This paper focuses primarily on the role of graph theory in the design of such a tool for the analysis of urban scene topology.; http://www.sciencedirect.com/science/article/B6V9K-4P6MPBP-2/1/e1b4066db2881db3de31085d779a27c4

Board interlocking, desempenho financeiro e valor das empresas brasileiras listadas em bolsa: análise sob a ótica da teoria dos grafos e de redes sociais; Board interlocking, financial performance and value of listed companies in brazilian stocks: analysis in the perspective of graph theory and social network

Mendes-da-Silva, Wesley
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 06/04/2010 PT
Relevância na Pesquisa
55.87%
A governança corporativa é uma área do conhecimento em finanças que tem recebido crescente atenção da comunidade acadêmica. Em seu escopo, existe um fenômeno que, crescentemente, tem motivado pesquisas: o board interlocking. Isto é, o fato de uma ou mais pessoas participarem, simultaneamente, do conselho de administração de empresas diferentes, possibilitando a formação de redes corporativas e pessoais, nas quais são criados fluxos de recursos essenciais à empresa, sejam esses negociados, ou não, em mercados. Diante desses argumentos, o objetivo principal desta tese é verificar a existência de associações de aspectos posicionais das empresas nas redes com o valor e o desempenho financeiro da firma, ao mesmo tempo em que se analisa a evolução estrutural das redes corporativas e pessoais. O presente estudo foi desenvolvido a partir de dados relativos a um conjunto de 452 empresas listadas no Brasil, entre 1997 e 2007, com base nas abordagens da teoria dos grafos e das redes sociais, empregando regressões com dados em painel. Os principais resultados deste estudo sugerem a existência de uma elite intelectual que ocupa a alta administração das companhias listadas em bolsa. Uma consequência desse resultado é o entendimento do ambiente corporativo...

Estratégias espaciais baseadas em ecologia de paisagens para a otimização dos esforços de restauração; Spatial strategies to optimize restoration efforts based on landscape ecology theory

Tambosi, Leandro Reverberi
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 20/02/2014 PT
Relevância na Pesquisa
55.99%
Os efeitos deletérios da perda e fragmentação de habitat são considerados a maior ameaça à manutenção da biodiversidade do planeta. Uma das maneiras de evitar a perda de espécies em paisagens fragmentadas é a restauração ecológica, que propicia tanto o aumento da quantidade quanto a melhoria da qualidade do habitat remanescente. Além de influenciar a persistência de espécies, as condições da paisagem são reconhecidas como importantes para o sucesso das ações de restauração. Entretanto, as diretrizes para incorporação das características da paisagem no planejamento da restauração são ainda ambíguas, não facilitando o processo de tomada de decisão. O presente trabalho teve como objetivo contribuir para o avanço do uso de análises espacialmente explícitas da estrutura da paisagem para o planejamento de ações de restauração. Para isso, foram elaboradas propostas metodológicas embasadas no atual conhecimento da ecologia de paisagens e foram realizadas simulações para comparar os potenciais benefícios para a biodiversidade resultantes de diferentes estratégias para seleção de áreas para restauração. A primeira proposta, apresentada no capítulo 2, utiliza análises de paisagens em múltiplas escalas...

Graph Laplacian for spectral clustering and seeded image segmentation; Estudo do Laplaciano do grafo para o problema de clusterização espectral e segmentação interativa de imagens

Casaca, Wallace Correa de Oliveira
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 05/12/2014 EN
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Image segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy functionals. The effectiveness of both segmentation algorithms is verified by visually evaluating the resulting partitions against state-of-the-art methods as well as through a variety of quantitative measures typically employed as benchmark by the image segmentation community. Our spectral-based segmentation algorithm combines image decomposition, similarity metrics, and spectral graph theory into a concise and powerful framework. An image decomposition is performed to split the input image into texture and cartoon components. Then, an affinity graph is generated and weights are assigned to the edges of the graph according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. Moreover...

Corte em grafos e segmentação de imagens utilizando um algoritmo aglomerativo de agrupamento hierárquico; Graph cut and image segmentation using an hierarquical agglomerative clustering algorithm

Elaine Ayumi Chiba
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 21/02/2014 PT
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56.04%
Representar os elementos de uma imagem em forma de grafos torna a estrutura organizada permitindo formular problemas de forma flexível e ser computacionalmente mais eficiente. Existem muitas técnicas da teoria de grafos sendo utilizadas em processamento digital de imagens. Em particular, o particionamento em grafos ou corte em grafos tem sido estudada por diversos autores como uma ferramenta de segmentação de imagens. Particionamento de um grafo refere-se à sua divisão em vários subgrafos tais que cada um deles representa um objeto de interesse na imagem. Neste trabalho, propomos um algoritmo de agrupamento hierárquico aglomerativo dos nós do grafo com base nas métricas de corte e corte médio. As segmentações foram avaliadas usando o benchmark da Berkeley BSDS500 que compara e classifica as segmentações em relação à outras técnicas existentes na literatura. Os resultados obtidos são promissores e nos permite concluir de que a combinação das métricas de corte e corte médio possibilitou melhores segmentações.; Representing the elements of an image in graphs makes the structure organized allowing to formulate problems in a flexible manner and can be more computationally efficient. There are many techniques of graph theory that are used in digital image processing. In particular...

Uso da teoria de grafos para seleção de modelos de reservatórios fraturados; Using graph theory to select models of fractured reservoirs

Alexandre de Lima
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 15/12/2014 PT
Relevância na Pesquisa
65.98%
A maior parte das reservas provadas de óleo convencional no mundo está contida nos reservatórios carbonáticos, as quais, em sua maioria, apresentam fraturas responsáveis por impactarem no fluxo do reservatório. Estas descontinuidades conhecidas como fraturas são encontradas na natureza em diversas escalas e, dependendo do tamanho, podem apresentar dificuldades para serem caracterizadas e modeladas matematicamente. Para exemplificar, pode ser citada a complexidade intrínseca à caracterização de fraturas subsísmicas para modelar objetos em escala menor do que a escala de dados de sísmica e poço. De maneira geral, as fraturas sempre foram um desafio devido a diversos motivos tais como o acréscimo no tempo computacional nas simulações e as dificuldades na caracterização. Estas preocupações se agravam pelo fato de que, na maior parte das vezes, os estudos em engenharia já são complexos, iterativos e consomem elevado tempo até sua finalização como, por exemplo, no processo de ajuste de histórico. Com a intenção de auxiliar e reduzir o tempo despendido nestes estudos é proposta a construção de uma ferramenta rápida capaz de selecionar modelos através do uso da teoria dos Grafos, antes de partir diretamente para onerosas simulações de reservatórios fraturados. Assim...

Quantification of uncertainty of performance measures using graph theory

Lopes, Isabel da Silva; Sousa, Sérgio; Nunes, Eusébio P.
Fonte: Universidade da Coruña Publicador: Universidade da Coruña
Tipo: Conferência ou Objeto de Conferência
Publicado em /10/2013 ENG
Relevância na Pesquisa
66.03%
In this paper, the graph theory is used to quantify the uncertainty generated in performance measures during the process of performance measurement. A graph is developed considering all the sources of uncertainty present in this process and their relationship. The permanent function of the matrix associated with the graph is used as the basis for determining an uncertainty index.; This work was financed with FEDER Funds by Programa Operacional Fatores de Competitividade – COMPETE and by National Funds by FCT –Fundação para a Ciência e Tecnologia, Project: FCOMP-01-0124-FEDER-022674.

Graph theory approach to quantify uncertainty of performance measures

Sousa, Sérgio; Lopes, Isabel da Silva; Nunes, Eusébio P.
Fonte: Center for Quality Publicador: Center for Quality
Tipo: Artigo de Revista Científica
Publicado em //2015 ENG
Relevância na Pesquisa
65.95%
In this work, the performance measurement process is studied to quantify the uncertainty induced in the resulting performance measure (PM). To that end, the causes of uncertainty are identified, analysing the activities undertaken in the three following stages of the performance measurement process: design and implementation, data collection and record, and determination and analysis. A quantitative methodology based on graph theory and on the sources of uncertainty of the performance measurement process is used to calculate an uncertainty index to evaluate the level of uncertainty of a given PM or (key) performance indicator. An application example is presented. The quantification of PM uncertainty could contribute to better represent the risk associated with a given decision and also to improve the PM to increase its precision and reliability.; FCT – Fundação para a Ciência e Tecnologia within the Project Scope: PEst- OE/EEI/UI0319/2014.

Automatic theory formation in graph theory

Pistori,Hemerson; Wainer,Jacques
Fonte: Sociedade Brasileira de Computação Publicador: Sociedade Brasileira de Computação
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/1999 EN
Relevância na Pesquisa
55.93%
This paper presents SCOT, a system for automatic theory construction in the domain of Graph Theory. Following on the footsteps of the programs ARE [9], HR [1] and Cyrano [6], concept discovery is modeled as search in a concept space. We propose a classification for discovery heuristics, which takes into account the main processes related to theory construction: concept construction, example production, example analysis, conjecture construction, and conjecture analysis.

Brain functional networks in syndromic and non-syndromic autism: a graph theoretical study of EEG connectivity

Peters, Jurriaan M.; Taquet, Maxime; Vega, Clemente; Jeste, Shafali S; Fernández, Iván; Tan, Jacqueline E; Nelson, Charles A.; Sahin, Mustafa; Warfield, Simon Keith
Fonte: Springer Science + Business Media Publicador: Springer Science + Business Media
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
55.99%
Background Graph theory has been recently introduced to characterize complex brain networks, making it highly suitable to investigate altered connectivity in neurologic disorders. A current model proposes autism spectrum disorder (ASD) as a developmental disconnection syndrome, supported by converging evidence in both non-syndromic and syndromic ASD. However, the effects of abnormal connectivity on network properties have not been well studied, particularly in syndromic ASD. To close this gap, brain functional networks of electroencephalographic (EEG) connectivity were studied through graph measures in patients with Tuberous Sclerosis Complex (TSC), a disorder with a high prevalence of ASD, as well as in patients with non-syndromic ASD. Methods EEG data were collected from TSC patients with ASD (n = 14) and without ASD (n = 29), from patients with non-syndromic ASD (n = 16), and from controls (n = 46). First, EEG connectivity was characterized by the mean coherence, the ratio of inter- over intra-hemispheric coherence and the ratio of long- over short-range coherence. Next, graph measures of the functional networks were computed and a resilience analysis was conducted. To distinguish effects related to ASD from those related to TSC...

Advanced hybrid approaches based on graph theory decomposition, modified evolutionary algorithms and deterministic optimisation techniques for the design of water distribution systems.

Zheng, Feifei
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado
Publicado em //2013
Relevância na Pesquisa
66.03%
The cost of water distribution system (WDS) design or rehabilitation is normally expensive. Over the past 40 years, a number of optimization¹ techniques have therefore been developed to find optimal designs for WDSs in order to save costs, while satisfying the specified design criteria. Often there are a large number of decision variables involved. The majority of currently available optimization techniques exhibit limitations when dealing with large WDSs. Two limitations include (i) finding only local optimal solutions and/or (ii) exhibiting computational inefficiency. The research undertaken in this dissertation has focused on developing advanced optimization techniques that are able to find good quality solutions for real-world sized or large WDS design or rehabilitation strategies with great efficiency. There were three objectives for the research: (i) the modification and improvement of currently available optimization techniques; (ii) the development of advanced hybrid optimization techniques (evolutionary algorithms combined with traditional deterministic optimization techniques) and (iii) the proposal of novel optimization methods with the incorporation of graph decomposition techniques. The most novel feature of this research is that graph decomposition techniques have been successfully incorporated to facilitate the optimization for WDS design. A number of decomposition techniques have been developed to decompose WDSs by the use of graph theory in this research. Real-world sized or large WDSs are used to demonstrate the effectiveness of the proposed advanced optimization techniques described in this thesis. Results show that these advanced methods are capable of obtaining sound optimal solutions with significantly improved efficiency compared to currently available optimization techniques. The main contribution of this thesis is the provision of effective and efficient optimization techniques for real-world sized or large WDS designs or rehabilitation problems. ¹American spelling has been used in this thesis as all the publications included in this thesis have been submitted to or published in American journals.; Thesis (Ph.D.) -- University of Adelaide...

Identifying Congestion in Software-Defined Networks Using Spectral Graph Theory

Parker, Thomas; Johnson, Jamie; Tummala, Murali; McEachen, John; Scrofani, James
Fonte: Escola de Pós-Graduação Naval Publicador: Escola de Pós-Graduação Naval
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.03%
Asilomar 2014; Software-defined networks (SDN) are an emerging technology that offers to simplify networking devices by centralizing the network layer functions and allowing adaptively programmable traffic flows. We propose using spectral graph theory methods to identify and locate congestion in a network. The analysis of the balanced traffic case yields an efficient solution for congestion identification. The unbalanced case demonstrates a distinct drop in connectivity that can be used to determine the onset of congestion. The eigenvectors of the Laplacian matrix are used to locate the congestion and achieve effective graph partitioning.

Orientações pfaffianas e o furtivo grafo de Heawood; Pfaffian orientations and the elusive Heawood graph

Alberto Alexandre Assis Miranda
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 07/08/2006 PT
Relevância na Pesquisa
56.06%
Um grafo G que tem emparelhamento perfeito é o Pfaffiano se existe uma orientação D das arestas de G, tal que todo circuito conforme de G tem orientação ímpar em D. Um subgrafo H de G é conforme se G- V (H) tem emparelhamento perfeito. Uma orientação de um circuito par é ímpar se numa dada direção de percurso do circuito o número de arestas que concorda com a direção é ímpar. Calcular o número de emparelhamentos perfeitos de um grafo, no caso geral, _e NP-difícil [11, pág. 307]. No entanto, para grafos Pfaffiano, seu cálculo torna-se polinomial [11, pág. 319]. A caracterização de grafos bipartidos Pfaffiano, feita por Little, tem quase trinta anos [9]. No entanto, somente nos últimos anos apareceram algoritmos polinomiais para reconhecimento de tais grafos, por McCuaig [13] e independentemente por Robertson, Seymour e Thomas [14]. A solução para este problema resolve também uma série de problemas, muitos deles clássicos, em teoria dos grafos, economia e química, como descrito no artigo de McCuaig [13, págs. 16 a 35]. Nesta dissertação, apresentamos uma prova de corretude do algoritmo distinta das duas provas anteriormente conhecidas; A graph G that contains a perfect matching is Pfaffiano if there is an orientation D of the edges of G...

Qubits from Adinkra Graph Theory via Colored Toric Geometry

Aadel, Y.; Belhaj, A.; Benslimane, Z.; Sedra, M. B.; Segui, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/06/2015
Relevância na Pesquisa
56.01%
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory. This one to one correspondence may be explored to attack qubit system problems using geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with \bf CP^1, \bf CP^1\times CP^1 and \bf CP^1\times CP^1\times CP^1 toric varieties respectively. Using a geometric procedure referred to as colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of Adinkra graph theory. Operations on toric information can produce universal quantum gates.; Comment: 13 pages, 2 figures

A Novel Analytical Method for Evolutionary Graph Theory Problems

Shakarian, Paulo; Roos, Patrick; Moores, Geoffrey
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/01/2013
Relevância na Pesquisa
55.95%
Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.

Extremal Graph Theory for Metric Dimension and Diameter

Hernando, Carmen; Mora, Merce; Pelayo, Ignacio M.; Seara, Carlos; Wood, David R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/05/2007
Relevância na Pesquisa
55.99%
A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$. Let $\mathcal{G}_{\beta,D}$ be the set of graphs with metric dimension $\beta$ and diameter $D$. It is well-known that the minimum order of a graph in $\mathcal{G}_{\beta,D}$ is exactly $\beta+D$. The first contribution of this paper is to characterise the graphs in $\mathcal{G}_{\beta,D}$ with order $\beta+D$ for all values of $\beta$ and $D$. Such a characterisation was previously only known for $D\leq2$ or $\beta\leq1$. The second contribution is to determine the maximum order of a graph in $\mathcal{G}_{\beta,D}$ for all values of $D$ and $\beta$. Only a weak upper bound was previously known.

Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory

Narayanan, Bhargav
Fonte: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics Publicador: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics
Tipo: Thesis; doctoral; PhD
EN
Relevância na Pesquisa
55.92%
In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.

Graph Theory and Dynamic Programming Framework for Automated Segmentation of Ophthalmic Imaging Biomarkers

Chiu, Stephanie Ja-Yi
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2014
Relevância na Pesquisa
65.95%

Accurate quantification of anatomical and pathological structures in the eye is crucial for the study and diagnosis of potentially blinding diseases. Earlier and faster detection of ophthalmic imaging biomarkers also leads to optimal treatment and improved vision recovery. While modern optical imaging technologies such as optical coherence tomography (OCT) and adaptive optics (AO) have facilitated in vivo visualization of the eye at the cellular scale, the massive influx of data generated by these systems is often too large to be fully analyzed by ophthalmic experts without extensive time or resources. Furthermore, manual evaluation of images is inherently subjective and prone to human error.

This dissertation describes the development and validation of a framework called graph theory and dynamic programming (GTDP) to automatically detect and quantify ophthalmic imaging biomarkers. The GTDP framework was validated as an accurate technique for segmenting retinal layers on OCT images. The framework was then extended through the development of the quasi-polar transform to segment closed-contour structures including photoreceptors on AO scanning laser ophthalmoscopy images and retinal pigment epithelial cells on confocal microscopy images.

The GTDP framework was next applied in a clinical setting with pathologic images that are often lower in quality. Algorithms were developed to delineate morphological structures on OCT indicative of diseases such as age-related macular degeneration (AMD) and diabetic macular edema (DME). The AMD algorithm was shown to be robust to poor image quality and was capable of segmenting both drusen and geographic atrophy. To account for the complex manifestations of DME...

Graph reconstruction numbers

McMullen, Brian
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Masters Project Formato: 300209 bytes; 88328 bytes; application/pdf; application/pdf
EN_US
Relevância na Pesquisa
56.05%
The Reconstruction Conjecture is one of the most important open problems in graph theory today. Proposed in 1942, the conjecture posits that every simple, finite, undirected graph with more than three vertices can be uniquely reconstructed up to isomorphism given the multiset of subgraphs produced by deleting each vertex of the original graph. Related to the Reconstruction Conjecture, reconstruction numbers concern the minimum number of vertex deleted subgraphs required to uniquely identify a graph up to isomorphism. During the summer of 2004, Jennifer Baldwin completed an MS project regarding reconstruction numbers. In it, she calculated reconstruction numbers for all graphs G where 2 < |V(G)| < 9. This project expands the computation of reconstruction numbers up to all graphs with ten vertices and a specific class of graphs with eleven vertices. Whereas Jennifer's project focused on a statistical analysis of reconstruction number results, we instead focus on theorizing the causes of high reconstruction numbers. Accordingly, this project establishes the reasons behind all high existential reconstruction numbers identified within the set of all graphs G where 2 < |V(G)| < 11 and identifies new classes of graphs that have large reconstruction numbers. Finally...

A Thermodynamics Approach to Graph Similarity

Robles-Kelly, Antonio
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
Relevância na Pesquisa
56.06%
In this paper, we describe the use of concepts from the areas of spectral-graph theory, kernel methods and differential geometry for the purposes of recovering a measure of similarity between pairs of graphical structures. To do this, we commence by relating each of the graphs under study to a Riemannian manifold through the use of the graph Laplacian and the heat operator. We do this by making use of the heat kernel and the set of initial conditions for the space of functions associated to the Laplace-Beltrami operator. With these ingredients, we make use of the first law of thermodynamics to recover the thermal energy associated to the conduction of heat through the graph. Thus, the problem of recovering a measure of similarity between pairs of graphs becomes that of computing the difference in their thermal energies. We illustrate the utility of the similarity metric recovered in this way for purposes of content-based image database indexing and retrieval.