This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, ...including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA
The local edge metric dimension of graph Adawiyah, R; Dafik; Alfarisi, R ...
Journal of physics. Conference series,
05/2020, Letnik:
1543, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG(e,v) = min{d(x,v),d(y,v)} is the ...distance between the vertex v and the edge xy in graph G. A non empty set S⊂V is an edge metric generator for G if for any two edges e1,e2∈E there is a vertex k∈S such that dG(k,e1≠dG(k,e2)). The minimum cardinality of edge metric generator for G is called as edge metric dimension of G, denoted by dimE(G). The local edge metric dimension of G, denoted by dimE(G), is a local edge metric generator of G if r(xk|S)≠r(yk|S) for every pair xk,ky of adjacent edges of G. Our concern in this paper is investigating some results of local edge metric dimension on some graphs.
The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard ...theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-experts in the subject.
The Geometry of Two-Weight Codes Over ℤ p m Shi, Minjia; Honold, Thomas; Sole, Patrick ...
IEEE transactions on information theory,
12/2021, Letnik:
67, Številka:
12
Journal Article
Recenzirano
We investigate fat projective linear codes over Formula Omitted, Formula Omitted, with two nonzero homogeneous weights (“two-weight codes”), building on the graph theory approach developed by ...Delsarte for codes over fields. Our main result is the classification of such codes under the additional assumption that the columns of a generator matrix of the code determine a cap in the projective Hjelmslev geometry Formula Omitted. This generalizes a result on projective two weight codes with dual distance at least four (Calderbank, 1982). The proof relies on a careful analysis of a certain strongly regular graph built on the cosets of the dual code, and on an interpretation of its parameters in terms of projective Hjelmslev geometry.
The average geodesic distance L Newman (2003) and the compactness C.sub.B Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for ...simple connected undirected graphs G of order n, we study the behavior of L(G) and C.sub.B (G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and C.sub.B (G) lies within the interval 0;1/3 and 2/3;1, respectively. Moreover, for any not necessarily rational number beta element of 0;1/3 (alpha element of 2/3;1) we show how to construct the sequence of graphs {G}, |V(G)| = n right arrow infinity, for which the limit of L(G)/n (C.sub.B (G)) is exactly beta (alpha) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.
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