Complex networks can be used for modeling street meshes and urban agglomerates. With such a model, many aspects of a city can be investigated to promote a better quality of life to its citizens. Along these lines, this paper proposes a set of distance-based pattern-discovery algorithmic instruments to improve urban structures modeled as complex networks, detecting nodes that lack access from to points of interest in a given city. Furthermore, we introduce a greedy algorithm that is able to recommend improvements to the structure of a city by suggesting where points of interest are to be placed. We contribute to a thorough process to deal with complex networks, including mathematical modeling and algorithmic innovation. The set of our contributions introduces a systematic manner to treat a recurrent problem of broad interest in cities.
The synergy of real-world systems can be described as complex networks that exchange information through their entities' relationships. Such networks can model complex systems from neuronal networks to subway systems @cite_7 and also, they can shape cities when linking the network topology with georeferenced data.
@cite_7
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Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes, rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular we propose a series of measures to characterize the multiplexicity of the systems in terms of: i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, ii) local properties such as the clustering coefficient and the transitivity, iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuine multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications and business relationships. Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering. © 2005 Elsevier B.V. All rights reserved. Many important real-world systems, modeled naturally as complex networks, have heterogeneous interactions and complicated dependency structures. Link prediction in such networks must model the influences between heterogenous relationships and distinguish the formation mechanisms of each link type, a task which is beyond the simple topological features commonly used to score potential links. In this paper, we introduce a novel probabilistically weighted extension of the Adamic Adar measure for heterogenous information networks, which we use to demonstrate the potential benefits of diverse evidence, particularly in cases where homogeneous relationships are very sparse. However, we also expose some fundamental flaws of traditional unsupervised link prediction. We develop supervised learning approaches for relationship (link) prediction in multi-relational networks, and demonstrate that a supervised approach to link prediction can enhance performance. We present results on three diverse, real-world heterogeneous information networks and discuss the trends and tradeoffs of supervised and unsupervised link prediction in a multi-relational setting. Networks of coupled dynamical systems have been used to model biological oscillators1,2,3,4, Josephson junction arrays5,6, excitable media7, neural networks8,9,10, spatial games11, genetic control networks12 and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them ‘small-world’ networks, by analogy with the small-world phenomenon13,14 (popularly known as six degrees of separation15). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.