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 …

Any permutation of ordered n-element set [n]=:{1,..., n} may be regarded as introducing a
(possibly null) measure of disorder to that set. For example, the natural order of [7] is …

Questions of 'how best to acquire data'are essential to modelling and prediction in the
natural and social sciences, engineering applications, and beyond. Optimal experimental …

Parameterized complexity/multivariate complexity algorithmics is an exciting field of modern
algorithm design and analysis, with a broad range of theoretical and practical aspects that …

Let 𝐺 be a graph with adjacency matrix 𝐴 (𝐺), and let 𝐷 (𝐺) be the diagonal matrix of the
degrees of 𝐺: The signless Laplacian 𝑄 (𝐺) of 𝐺 is defined as 𝑄 (𝐺)≔ 𝐴 (𝐺)+ 𝐷 (𝐺) …

This beginning graduate textbook describes both recent achievements and classical results
of computational complexity theory. Requiring essentially no background apart from …

This concise and self-contained introduction builds up the spectral theory of graphs from
scratch, with linear algebra and the theory of polynomials developed in the later parts. The …

Although this may seem a paradox, all exact science is dominated by the idea of
approximation. Bertrand Russell (1872-1970) Most natural optimization problems, including …

Various aspects of the theory of random walks on graphs are surveyed. In particular,
estimates on the important parameters of access time, commute time, cover time and mixing …

Graph Theory has proved to be an extremely useful tool for solving combinatorial problems
in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations …