Topology of Brain Functional Networks: Towards the Role of Genes M´ aria Markoˇ sov´a 1 , Liz Franz 2 , and ˇ Lubica Beˇ nuˇ skov´a 3 1 Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 2 Department of Psychology 3 Department of Computer Science, University of Otago, Dunedin, New Zealand lubica@cs.otago.ac.nz Abstract. We have extracted brain functional networks from fMRI data based on temporal correlations of voxel activities during the rest and task periods. The goal of our preliminary research was to study the topol- ogy of these networks in terms of small-world and scale-free properties. The small-world property was quite clearly evident whereas the scale- free character was less obvious, especially in the rest condition. In ad- dition, there were some differences between the rest and task functional brain networks as well as between subjects. We discuss the relation of properties of functional brain networks to the topological properties of the underlying anatomical networks, which are largely dependent upon genetic instructions during brain development. 1 Introduction Functional magnetic resonance imaging (fMRI) is a powerful noninvasive tech- nique of brain activity imaging [1]. A measure of brain activity is the blood oxygenation level dependent (BOLD) signal recorded sequentially in slices of thousands of voxels of ∼ 3 mm 3 over the whole brain within the interval of 2–3 sec. In addition to valuable information on localization of various brain func- tions, it is possible to analyze the data to seek the underlying functional brain networks, i.e. networks of functional units that temporarily self-organize them- selves to engage in a given task or to engage in spontaneous background activity during the rest condition. In general, a network is a set of nodes linked by edges, oriented or not, math- ematically described as a directed or undirected graph, respectively. Recently, Chialvo with co workers [2] [3] introduced the concepts from the graph theory to study the topological structure of functional brain networks. Topology is not concerned with metric properties such as physical distances between nodes, in- stead, topology involves the study of properties that describe how the nodes are assembled in space through their interconnections. Basic concepts from the graph theory used to describe the network topology are the degree k, clustering coefficient C, average shortest path L and degree M. K¨oppen et al. (Eds.): ICONIP 2008, Part I, LNCS 5506, pp. 111–118, 2009. c  Springer-Verlag Berlin Heidelberg 2009