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24
CONTEST: A controllable test matrix toolbox for MATLAB
 ACM Trans. Math. Software
, 2008
"... Networks describing connectivity structures arise across a vast range of application areas. Examples where it has proved useful to record data include interactions between genes [Kauffman 1969], proteins [de Silva and Stumpf 2005], cortical regions [Kamper et al. 2002; Sporns and Zwi 2004], internet ..."
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Cited by 17 (2 self)
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Networks describing connectivity structures arise across a vast range of application areas. Examples where it has proved useful to record data include interactions between genes [Kauffman 1969], proteins [de Silva and Stumpf 2005], cortical regions [Kamper et al. 2002; Sporns and Zwi 2004], internet nodes [Faloutsos et al. 1999], web pages [Broder et al. 2000; Page et al. 1998], countries [Fagiolo 2007], coauthors [Newman 2004], telephones [Abello et al. 1998], assets on the stock market [Boginski
LOCAL OPTIMIZATION FOR GLOBAL ALIGNMENT OF PROTEIN INTERACTION NETWORKS
"... We propose a novel algorithm, PISwap, for computing global pairwise alignments of protein interaction networks, based on a local optimization heuristic that has previously demonstrated its effectiveness for a variety of other NPhard problems, such as the Traveling Salesman Problem. Our algorithm be ..."
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We propose a novel algorithm, PISwap, for computing global pairwise alignments of protein interaction networks, based on a local optimization heuristic that has previously demonstrated its effectiveness for a variety of other NPhard problems, such as the Traveling Salesman Problem. Our algorithm begins with a sequencebased network alignment and then iteratively adjusts the alignment by incorporating network structure information. It has a worstcase pseudopolynomial runningtime bound and is very efficient in practice. It is shown to produce improved alignments in several wellstudied cases. In addition, the flexible nature of this algorithm makes it suitable for different applications of network alignments. Finally, this algorithm can yield interesting insights into the evolutionary history of the compared species.
Spatial models for virtual networks
"... Abstract. This paper discusses the use of spatial graph models for the analysis of networks that do not have a direct spatial reality, such as web graphs, online social networks, or citation graphs. In a spatial graph model, nodes are embedded in a metric space, and link formation depends on the re ..."
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Cited by 8 (5 self)
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Abstract. This paper discusses the use of spatial graph models for the analysis of networks that do not have a direct spatial reality, such as web graphs, online social networks, or citation graphs. In a spatial graph model, nodes are embedded in a metric space, and link formation depends on the relative position of nodes in the space. It is argued that spatial models form a good basis for link mining: assuming a spatial model, the link information can be used to infer the spatial position of the nodes, and this information can then be used for clustering and recognition of node similarity. This paper gives a survey of spatial graph models, and discusses their suitability for link mining. 1
Some typical properties of the Spatial Preferred Attachment model
 Proceedings of the 9th Workshop on Algorithms and Models for the Web Graph (WAW 2012), Lecture Notes in Computer Science 7323
, 2012
"... Abstract. We investigate a stochastic model for complex networks, based on a spatial embedding of the nodes, called the Spatial Preferred Attachment (SPA) model. In the SPA model, nodes have spheres of influence of varying size, and new nodes may only link to a node if they fall within its influence ..."
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Abstract. We investigate a stochastic model for complex networks, based on a spatial embedding of the nodes, called the Spatial Preferred Attachment (SPA) model. In the SPA model, nodes have spheres of influence of varying size, and new nodes may only link to a node if they fall within its influence region. The spatial embedding of the nodes models the background knowledge or identity of the node, which influences its link environment. In this paper, we focus on the (directed) diameter, small separators, and the (weak) giant component of the model. 1.
Diameter and Broadcast Time of Random Geometric Graphs in Arbitrary Dimensions
 ALGORITHMICA
, 2012
"... A random geometric graph (RGG) is defined by placing n points uniformly at random in [0,n1/d] d, and joining two points by an edge whenever their Euclidean distance is at most some fixed r. We assume that r is larger than the critical value for the emergence of a connected component with Ω(n) nodes ..."
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A random geometric graph (RGG) is defined by placing n points uniformly at random in [0,n1/d] d, and joining two points by an edge whenever their Euclidean distance is at most some fixed r. We assume that r is larger than the critical value for the emergence of a connected component with Ω(n) nodes. We show that, with high probability (w.h.p.), for any two connected nodes with a Euclidean log n distance of ω( rd−1), their graph distance is only a constant factor larger than their Euclidean distance. This implies that the diameter of the largest connected component is Θ(n1/d /r) w.h.p. We also prove that the condition on the Euclidean distance above is essentially tight. We also analyze the following randomized broadcast algorithm on RGGs. At the beginning, only one node from the largest connected component of the RGG is informed. Then, in each round, each informed node chooses a neighbor independently and uniformly at random and informs it. We prove that w.h.p. this algorithm informs every node in the largest connected component of an RGG within Θ(n1/d /r + log n) rounds.
MODEL SELECTION FOR SOCIAL NETWORKS USING GRAPHLETS
"... Abstract. Several network models have been proposed to explain the link structure observed in online social networks. This paper addresses the problem of choosing the model that best fits a given real world network. We implement a model selection method based on unsupervised learning. An alternatin ..."
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Abstract. Several network models have been proposed to explain the link structure observed in online social networks. This paper addresses the problem of choosing the model that best fits a given real world network. We implement a model selection method based on unsupervised learning. An alternating decision tree is trained using synthetic graphs generated according to each of the models under consideration. We use a broad array of features, with the aim of representing different structural aspects of the network. Features include the frequency counts of small subgraphs (graphlets) as well as features capturing the degree distribution and small world property. Our method correctly classifies synthetic graphs, and is robust under perturbations of the graphs. We show that the graphlet counts alone are sufficient in separating the training data, indicating that graphlet counts are a good way of capturing network structure. We tested our approach on four Facebook graphs from various American Universities. The models that best fit this data are those that are based on the principle of preferential attachment. 1.
Geometric Graph Properties of the Spatial Preferred Attachment model
, 2012
"... The spatial preferred attachment (SPA) model is a model for networked information spaces such as domains of the World Wide Web, citation graphs, and online social networks. It uses a metric space to model the hidden attributes of the vertices. Thus, vertices are elements of a metric space, and link ..."
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The spatial preferred attachment (SPA) model is a model for networked information spaces such as domains of the World Wide Web, citation graphs, and online social networks. It uses a metric space to model the hidden attributes of the vertices. Thus, vertices are elements of a metric space, and link formation depends on the metric distance between vertices. We show, through theoretical analysis and simulation, that for graphs formed according to the SPA model it is possible to infer the metric distance between vertices from the link structure of the graph. Precisely, the estimate is based on the number of common neighbours of a pair of vertices, a measure known as cocitation. To be able to calculate this estimate, we derive a precise relation between the number of common neighbours and metric distance. We also analyze the distribution of edge lengths, where the length of an edge is the metric distance between its end points. We show that this distribution has three different regimes, and that the tail of this distribution follows a power law.
Graph analysis and visualization for brain function characterization using EEG data
 J. Healthcare Eng
, 2010
"... ABSTRACT Over the past few years, there has been an increased interest in studying the underlying neural mechanism of cognitive brain activity as well as in diagnosing certain pathologies. Noninvasive imaging modalities such as functional magnetic resonance imaging (fMRI), positron emission tomogra ..."
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ABSTRACT Over the past few years, there has been an increased interest in studying the underlying neural mechanism of cognitive brain activity as well as in diagnosing certain pathologies. Noninvasive imaging modalities such as functional magnetic resonance imaging (fMRI), positron emission tomography (PET), and dynamic signal acquisition techniques such as quantitative electroencephalography (EEG) have been vastly used to estimate cortical connectivity and identify functional interdependencies among synchronized brain lobes. In this area, graphtheoretic concepts and tools are used to describe large scale brain networks while performing cognitive tasks or to characterize certain neuropathologies. Such tools can be of particular value in basic neuroscience and can be potential candidates for future inclusion in a clinical setting. This paper discusses the application of the high time resolution EEG to resolve interdependence patterns using both linear and nonlinear techniques. The network formed by the statistical dependencies between the activations of distinct and often well separated neuronal populations is further analyzed using a number of graph theoretic measures capable of capturing and quantifying its structure and summarizing the information that it contains. Finally, graph visualization reveals the hidden structure of the networks and amplifies human understanding. A number of possible applications of the graph theoretic approach are also listed. A freely available standalone brain visualization tool to benefit the healthcare engineering community is also provided
Characterizing the Structural Complexity of RealWorld Complex Networks
"... Abstract. Although recent research has shown that the complexity of a network depends on its structural organization, which is linked to the functional constraints the network must satisfy, there is still no systematic study on how to distinguish topological structure and measure the corresponding s ..."
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Abstract. Although recent research has shown that the complexity of a network depends on its structural organization, which is linked to the functional constraints the network must satisfy, there is still no systematic study on how to distinguish topological structure and measure the corresponding structural complexity of complex networks. In this paper, we propose the first consistent framework for distinguishing and measuring the structural complexity of realworld complex networks. In terms of the smallest d of the dK model with highorder constraints necessary for fitting real networks, we can classify realworld networks into different structural complexity levels. We demonstrate the approach by measuring and classifying a variety of realworld networks, including biological and technological networks, smallworld and nonsmallworld networks, and spatial and nonspatial networks.