My current research is focused on complex networks, centered around the idea of representing the system under study with a graph, capturing the web of connections among the units it is made of. I am particularly intereseted in hierarchical networks, tagged netwokrs, general random graph generators, community evolution and community finding in general.
Hierarchical networks
Hierarchical organisation is a prevalent feature in networks representing various systems from nature and society, where the nodes are organised according to a pyramidal structure, with decision makers at the top and followers at the bottom. While this phenomenon is widespread, the underlying governing principles are poorly understood, offering a plenty of interesting research topics. E.g., even the quantification of the extent of hierarchy in the structure of a general directed network is non-trivial, shown by the numerous alternative propositions for hierarchy measures in the scientific literature. Another interesting question is how may an initially non-hierarchical network evolve into a hierarchy over time, and what are the features of time evolving hierarchical networks we can observe in nature and in the society?
Tag hierarchies, folksonomies
The voluntary tagging of various items (e.g., books, films, photos, etc.) with free words has become a popular way of summarising their most important aspects in a wide range of online platforms from web-stores (e.g., Amazon) to tagging systems (e.g., Flickr). The emerging collections of tagged objects are often called as folksonomies, referring to the collaborative and self-organising nature of these systems, lacking any centralised control over the tags distributed by the users. Folksonmies provide a very interesting direction for research, especially when compared to ontologies and other types of tagged networks where the tags are organised into a hierarchy. E.g., a challenge with great potential for practical applications is extracting an ontology from a folksonomy simply by analysing the statistical properties of the tags.
For more info, please visit our website dedicated to tag hierarchy extraction, where you can also download our hierarchy extraction algorithms, tagged data sets, etc..

Multifractals and radom graphs
Random graph models have always played a central role in the description of complex networks and serve as a basic tool for generating artificial networks which be used to test hypotheses, or, as models of actual data. However, most of the models concentrate only on a particular aspect of networks (e.g., clustering, a given degree distribution, etc.), and for each newly discovered feature a new model has to be constructed. Due to this proliferation of network models, the concept of general network models and methods for generating graphs with desired properties has attracted great interest lately. Beside a couple of other interesting methods, a recently introduced approach along this line is the multifractal network generator, which was shown to be capable of generating a wide variety of network types with prescribed statistical properties, (e.g., with degree- or clustering coefficient distributions of various, very different forms). At the heart of this method lies a mapping between 2d measures defined on the unit square and random graphs. The main idea is to iterate a suitably chosen self similar multifractal (becoming singular in the limiting case) and enlarge the size of the generated graph (becoming infinite in the limiting case) in parallel. A very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured.

Communities, modules, clusters
Communities (also called as clusters, modules, or cohesive groups) correspond to more highly interconnected parts in networks with no widely accepted unique definition. Probably the best way to introduce the concept of communities is to give examples such as a family or a friendship circle in a social network, a group of densely interlinked web-pages with the same topic, a protein complex in a protein interaction network, or an industrial sector in economy. Communities provide an intermediate level of organisation in networks between the level of nodes (and motifs) and the level of the whole system. Due to their importance, a vast number of different community finding method have been introduced in the last decade. An intuitive alternative based on a local community definition is provided by the clique percolation method (CPM), allowing also overlaps between the communities. The main concept of this approach is to build up the communities from k-cliques, (corresponding to complete sub-graphs of size k), in order to ensure the high link density inside the communities. Two k-cliques are adjacent if they share k-1 nodes, and a community is equivalent to a percolation cluster of k-cliques, in which any k-clique can be reached from any other k-clique via sequences of k-clique adjacency. This method has been shown to provide meaningful overlapping communities in many systems, ranging from protein interaction networks through technological networks to social networks.
Go to our clustering page for more info on CPM, where you can also try out CFinder, a CPM based community finding and visualizing software.

Community evolution
Although the majority of community oriented studies concern static partitions, in fact the community structure is subject to constant evolution in many systems. E.g., social networks are always changing due to new acquaintances forming and older relationships fading away as time goes on. The rewiring of the underlying network naturally leads to the restructuring of the communities, which can grow by recruiting new members, or contract by loosing members; two (or more) communities may merge into a single community, while a large enough community can split into several smaller ones; new communities are born and old ones may disappear. Tracking time dependent communities is a non-trivial challenge in its own, and the study of the principles governing the community evolution is a very interesting direction for research in the fields of complex networks.
Go to our clustering page for more info on community evolution, where you can also try out CFinder, a CPM based community finding and visualizing software.
Gergely Palla
Senior Research Associate 

Statistical and Biological Physics 
Resarch Group of HAS,
Eötvös University,
Pázmány P. stny. 1/A
1117 Budapest, Hungary

Tel: +36-1-3722768
Fax: +36-1-3722752

Selected publications