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Exponential Random Graph Modeling for Complex Brain Networks  [PDF]
Sean L. Simpson,Satoru Hayasaka,Paul J. Laurienti
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0020039
Abstract: Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks.
Modeling Social Networks with Node Attributes using the Multiplicative Attribute Graph Model  [PDF]
Myunghwan Kim,Jure Leskovec
Computer Science , 2011,
Abstract: Networks arising from social, technological and natural domains exhibit rich connectivity patterns and nodes in such networks are often labeled with attributes or features. We address the question of modeling the structure of networks where nodes have attribute information. We present a Multiplicative Attribute Graph (MAG) model that considers nodes with categorical attributes and models the probability of an edge as the product of individual attribute link formation affinities. We develop a scalable variational expectation maximization parameter estimation method. Experiments show that MAG model reliably captures network connectivity as well as provides insights into how different attributes shape the network structure.
Random Graph Generator for Bipartite Networks Modeling  [PDF]
Szymon Chojnacki,Mieczys?aw K?opotek
Computer Science , 2010,
Abstract: The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of parameters.We adapt the advances of last decade in unipartite complex networks modeling to the bigraph setting. This data structure can be observed in several situations. However, only a few datasets are freely available to test the algorithms (e.g. community detection, influential nodes identification, information retrieval) which operate on such data. Therefore, artificial datasets are needed to enhance development and testing of the algorithms. We are particularly interested in applying the generator to the analysis of recommender systems. Therefore, we focus on two characteristics that, besides simple statistics, are in our opinion responsible for the performance of neighborhood based collaborative filtering algorithms. The features are node degree distribution and local clustering coeficient.
From time series to complex networks: the visibility graph  [PDF]
Lucas Lacasa,Bartolo Luque,Fernando Ballesteros,Jordi Luque,Juan Carlos Nuno
Physics , 2008, DOI: 10.1073/pnas.0709247105
Abstract: In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined in order to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.
Modeling Network Evolution Using Graph Motifs  [PDF]
Drew Conway
Computer Science , 2011,
Abstract: Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of several organization is also of interest to many researchers, such as the affiliations of legislators or the relationships among terrorist. A key aspect of studying social networks is understanding the evolutionary dynamics and the mechanism by which these structures grow and change over time. While current methods are well suited to describe static features of networks, they are less capable of specifying models of change and simulating network evolution. In the following paper I present a new method for modeling network growth and evolution. This method relies on graph motifs to generate simulated network data with particular structural characteristic. This technique departs notably from current methods both in form and function. Rather than a closed-form model, or stochastic implementation from a single class of graphs, the proposed "graph motif model" provides a framework for building flexible and complex models of network evolution. The paper proceeds as follows: first a brief review of the current literature on network modeling is provided to place the graph motif model in context. Next, the graph motif model is introduced, and a simple example is provided. As a proof of concept, three classic random graph models are recovered using the graph motif modeling method: the Erdos-Renyi binomial random graph, the Watts-Strogatz "small world" model, and the Barabasi-Albert preferential attachment model. In the final section I discuss the results of these simulations and subsequent advantage and disadvantages presented by using this technique to model social networks.
Large-scale inference and graph theoretical analysis of gene-regulatory networks in B. stubtilis  [PDF]
C. Christensen,A. Gupta,C. D. Maranas,R. Albert
Quantitative Biology , 2006, DOI: 10.1016/j.physa.2006.04.118
Abstract: We present the methods and results of a two-stage modeling process that generates candidate gene-regulatory networks of the bacterium B. subtilis from experimentally obtained, yet mathematically underdetermined microchip array data. By employing a computational, linear correlative procedure to generate these networks, and by analyzing the networks from a graph theoretical perspective, we are able to verify the biological viability of our inferred networks, and we demonstrate that our networks' graph theoretical properties are remarkably similar to those of other biological systems. In addition, by comparing our inferred networks to those of a previous, noisier implementation of the linear inference process [17], we are able to identify trends in graph theoretical behavior that occur both in our networks as well as in their perturbed counterparts. These commonalities in behavior at multiple levels of complexity allow us to ascertain the level of complexity to which our process is robust to noise.
An exponential random graph modeling approach to creating group-based representative whole-brain connectivity networks  [PDF]
Sean L. Simpson,Malaak N. Moussa,Paul J. Laurienti
Quantitative Biology , 2011,
Abstract: Group-based brain connectivity networks have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Accurately constructing these networks presents a daunting challenge given the difficulties associated with accounting for inter-subject topological variability. Viable approaches to this task must engender networks that capture the constitutive topological properties of the group of subjects' networks that it is aiming to represent. The conventional approach has been to use a mean or median correlation network (Achard et al., 2006; Song et al., 2009) to embody a group of networks. However, the degree to which their topological properties conform with those of the groups that they are purported to represent has yet to be explored. Here we investigate the performance of these mean and median correlation networks. We also propose an alternative approach based on an exponential random graph modeling framework and compare its performance to that of the aforementioned conventional approach. Simpson et al. (2010) illustrated the utility of exponential random graph models (ERGMs) for creating brain networks that capture the topological characteristics of a single subject's brain network. However, their advantageousness in the context of producing a brain network that "represents" a group of brain networks has yet to be examined. Here we show that our proposed ERGM approach outperforms the conventional mean and median correlation based approaches and provides an accurate and flexible method for constructing group-based representative brain networks.
Dynamic Networks from Hierarchical Bayesian Graph Clustering  [PDF]
Yongjin Park,Cristopher Moore,Joel S. Bader
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0008118
Abstract: Biological networks change dynamically as protein components are synthesized and degraded. Understanding the time-dependence and, in a multicellular organism, tissue-dependence of a network leads to insight beyond a view that collapses time-varying interactions into a single static map. Conventional algorithms are limited to analyzing evolving networks by reducing them to a series of unrelated snapshots.
Group Measures and Modeling for Social Networks  [PDF]
Vincent Levorato
Journal of Complex Systems , 2014, DOI: 10.1155/2014/354385
Abstract: Social network modeling is generally based on graph theory, which allows for study of dynamics and emerging phenomena. However, in terms of neighborhood, the graphs are not necessarily adapted to represent complex interactions, and the neighborhood of a group of vertices can be inferred from the neighborhoods of each vertex composing that group. In our study, we consider that a group has to be considered as a complex system where emerging phenomena can appear. In this paper, a formalism is proposed to resolve this problematic by modeling groups in social networks using pretopology as a generalization of the graph theory. After giving some definitions and examples of modeling, we show how some measures used in social network analysis (degree, betweenness, and closeness) can be also generalized to consider a group as a whole entity. 1. Introduction Network modeling is an area of research which covers several domains like computer sciences, physics, sociology, or biology. In social networks modeling, graphs are often used to describe the links representing relationships or flows between entities [1]. Based on graph theory, the studies consider in most cases individuals as single elements, a group being formed by several persons interacting with each other. Most of the few works on modeling groups in social networks consider a group as a combination of persons [2], not as a whole entity. As social network analysis leads to centrality notion and others sociometric features, what about group centrality? The centrality of a vertex in a graph is widely used to determine the relative “importance” of this vertex within the network [3]. Centrality measures enable us to find users who are extensively involved in relationships with other network members. There are different centralities such as degree centrality, betweenness centrality, or closeness centrality. The problem we face is the following: analyzing a vertex can be done with this kind of measure, but if we analyze a group of persons using the same measure, we will have no particular emergence of characteristics as the union property of the neighborhoods in a graph is preserved. As social networks are complex networks [4–6], emergence of phenomena can occur [7], and the behavior of a group of persons can be different from the “sum” of the person behaviors composing the group. Some work tried to capture the different scales of a network, and a group can be viewed as a community [8]; thus, in our opinion, graph theory only is inadequate to model all complex interactions occurring in a social network. Some
Modeling Emotion Influence from Images in Social Networks  [PDF]
Xiaohui Wang,Jia Jia,Lianhong Cai,Jie Tang
Computer Science , 2014,
Abstract: Images become an important and prevalent way to express users' activities, opinions and emotions. In a social network, individual emotions may be influenced by others, in particular by close friends. We focus on understanding how users embed emotions into the images they uploaded to the social websites and how social influence plays a role in changing users' emotions. We first verify the existence of emotion influence in the image networks, and then propose a probabilistic factor graph based emotion influence model to answer the questions of "who influences whom". Employing a real network from Flickr as experimental data, we study the effectiveness of factors in the proposed model with in-depth data analysis. Our experiments also show that our model, by incorporating the emotion influence, can significantly improve the accuracy (+5%) for predicting emotions from images. Finally, a case study is used as the anecdotal evidence to further demonstrate the effectiveness of the proposed model.
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