We propose a methodological framework to study the dynamics of inter-regional investment flow in Europe from a Complex Networks perspective, an approach with recent proven success in many fields including economics. In this work we study the network of investment stocks in Europe at two different levels: first, we compute the inward-outward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inward-outward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. Despite the intuitive value of this approach for EU policy making in economic development, to our knowledge there are no similar works in the literature yet. In this paper we focus on statistical distributions and scaling laws of activity, investment stock and connectivity degree both at the level of firms and at the level of regions. In particular we find that investment stock of firms is power law distributed with an exponent very close to the one found for firm activity. On the other hand investment stock and activity of regions turn out to be log-normal distributed. At both levels we find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales with connectivity in a similar way as has been previously found for stock market data, calling for further investigations on a possible general scaling law holding true in economical networks. Comment: 27 pages, 17 figures