Work group

As part of the COBRA research group, I lead a focused subgroup working on the methodology and theoretical foundations of complex networks and the processes associated with them. The group includes:

David Hartman	Head of the subgroup
General interest in complex networks and processes defined on them. Specific interests in theoretical foundations as well as applications of the studied phenomena.
Tomáš Hons	group member
they work on the theoretical foundations of complex networks, primarily in the areas of graph limits and root-finding problems in information propagation, as well as in the areas of graph classes and structural graph theory.
Aneta Pokorná	group member
they work in the field of structural theory of complex networks, focusing on network centrality, specifically rooted motifs and approximate symmetry.
David Kubek	group member
they work in the fields of network optimization, network process analysis, information propagation, and related information theory. In addition, they specialize in the field of optimization.
František Szczepanik	group member
They specialize in the structural description of networks and the related effects on network processes.
Past members
There were several members who contributed to the development of the group and its research, but have since moved on to other projects or institutions. Their contributions are still valued and appreciated. Anna Kmentová - worked on the comparison of information spreading algorithms František Miroslav Škola - worked on the symmetry of stock networks Daniel Trlifaj - worked on the theory of network graphlets
Collaborators from COBRA group	collaborative colleagues
Since our group is part of the COBRA group, which focuses on the broad application of complex networks to various types of data, we collaborate with its other members.

Group areas of interests

The unifying scientific concept of the research group is the formulation of complex network (CN)theory and the development of methods for related analyses of real-world systems. The group’s core activities focus on the following thematic areas.

• Properties of CN characteristics for specific classes of graphs
• Processes on networks and corresponding optimization problems
• Desining algorithms for CN
• Solution of real-world problem having network structure by novel approaches from CN

Following are some selected topics of interest within these areas:

Group particular topics

Symmetry in Complex Networks

Analysis of approximate network symmetry for networks or their components with an asymmetric structure. Within this area the interesting parts are

• Approximate symmetry in complex networks
• Efficient algorithms for approximate symmetry computation

The analysis of symmetrical relational structures and particularly those meeting homogeneity condition. Within this area the interesting parts are:

• Homomorphism-homogeneity of various structures
• Classes defined by various types of homogeneity
• Relational and lift complexity

Processes on Networks

The study of processes on networks, primarily algorithms for the spread of (dis)information, diseases, or opinions in (online) social networks. The influence of network structure on the nature of the spread.

• Design of efficient algorithms of for generalized (multilayerd) networks
• Properties of spreading process based on network structure

Study of problems related to root fining in large graphs, where the main areas are:

• Rooting vertices in classes of graphs and their limits
• Related Gadget construction in modellings

Structural properties of CN

A study of network characteristics, particularly graph centrality, and their properties in various classes of graphs.

• Network graphlets and their descriptive power with potential reconstruction
• Graphs with uniform betweenness centrality distribution

Optimization and interval optimization

Another area is area of optimization including matrix properties and interval optimization, where the main areas are:

• Absolute value linear programming
• Interval spectral decomposition and interval matrix powers

Real-world system characterization and optimization

Last area is that of dynamical systems with application to neurology, climatology, and energy where the main area of interests are:

• Effect of network structure on brain function, disease or behavior
• Handling complicated phenomena in climate using complex networks
• Using principles to characterize energy distribution systems

The results from these areas can be found at publication page.

Recent conferences

• Homomorphism-homogeneity classes of countable L -colored graphs, EUROCOMB 2019, Bratislava, Slovakia, 2019
• Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds, WCGO 2019, Mety, France, 2019
• Complexity of computing powers for various classes of interval matrices, MATTRIAD 2019, Liblice, Czech Republic, 2019
• Plausible ways to compute powers of interval matrices, ICMAA 2019, Reno, Nevada, 2019
• On equality of two classes of homomorphism-homogeneous relational structures, BANFF 2018 Unifying Themes in Ramsey Theory, Banff, 2018
• Equality of classes MH and HH, ICMS 2018 From permutation groups to model theory workshop, Edingurgh, 2018
• Computing powers of interval matrices, SCAN 2018, Tokyo, 2018
• Disturbing effects within construction of stock networks, Dresden, Germany, 2018