Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

/pdf/the-structure-and-function-of-complex-networks-34deompc9l.pdf

The Structure and Function of Complex Networks

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

http://brainimaging.waisman.wisc.edu/~chung/neuro.processing/literature/rubinov.2010.NI.network.pdf

Complex network measures of brain connectivity: uses and interpretations.

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

/pdf/community-detection-in-graphs-34rogm3r6p.pdf

Community detection in graphs

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a s...

https://arxiv.org/pdf/cond-mat/0505185.pdf

Characterization of complex networks: A survey of measurements

Many putative genetic factors that confer risk to neurodevelopmental disorders such as autism spectrum disorders (ASDs) and X-linked intellectual disability (XLID), and to neuropsychiatric disorders including attention deficit hyperactivity disorder (ADHD) and schizophrenia (SZ) have been identified in individuals from diverse human populations. Although there is significant aetiological heterogeneity within and between these conditions, recent data show that genetic factors contribute to their comorbidity. Many studies have identified candidate gene associations for these mental health disorders, albeit this is often done in a piecemeal fashion with little regard to the inherent molecular complexity. Here, we sought to abstract relationships from our knowledge of systems level biology to help understand the unique and common genetic drivers of these conditions. We undertook a global and systematic approach to build and integrate available data in gene networks associated with ASDs, XLID, ADHD and SZ. Complex network concepts and computational methods were used to investigate whether candidate genes associated with these conditions were related through mechanisms of gene regulation, functional protein-protein interactions, transcription factor (TF) and microRNA (miRNA) binding sites. Although our analyses show that genetic variations associated with the four disorders can occur in the same molecular pathways and functional domains, including synaptic transmission, there are patterns of variation that define significant differences between disorders. Of particular interest is DNA variations located in intergenic regions that comprise regulatory sites for TFs or miRNA. Our approach provides a hypothetical framework, which will help discovery and analysis of candidate genes associated with neurodevelopmental and neuropsychiatric disorders.

/pdf/neurodevelopmental-and-neuropsychiatric-disorders-represent-57dmwulsdx.pdf

Neurodevelopmental and neuropsychiatric disorders represent an interconnected molecular system

The estimation of the number of people in an area under surveillance is very important for the problem of crowd monitoring. When an area reaches an occupation level greater than the projected one, people's safety can be in danger. This paper describes a new technique for crowd density estimation based on Minkowski fractal dimension. The fractal dimension has been widely used to characterize data texture in a large number of physical and biological sciences. The results of our experiments show that fractal dimension can also be used to characterize levels of people congestion in images of crowds. The proposed technique is compared with a statistical and a spectral technique, in a test study of nearly 300 images of a specific area of the Liverpool Street Railway Station, London, UK. Results obtained in this test study are presented.

Estimating crowd density with Minkowski fractal dimension

https://ic.unicamp.br/~afalcao/mo815-grafos/a17.pdf

L. da F. Costa

Papers

Characterization of complex networks: A survey of measurements

Neurodevelopmental and neuropsychiatric disorders represent an interconnected molecular system

Estimating crowd density with Minkowski fractal dimension

A graph-based approach for multiscale shape analysis

Accessibility in complex networks