OPTIMIZATION of FLOW and CASCADING EFFECTS in WEIGHTED COMPLEX NETWORKS

2. Social sciences have the longest history of the substantial quantitative study of real-world networks. Acquaintance network, collaboration network of film actors, coauthorship networks. They shared many common features irrespective of their various origin. One of these was the highly irregular structure compared to a highly regular structure of a lattice. Social sciences have the longest history of the substantial quantitative study of real-world networks. Acquaintance network, collaboration network of film actors, coauthorship networks. They shared many common features irrespective of their various origin. One of these was the highly irregular structure compared to a highly regular structure of a lattice.

3. A different representation of the Internet is obtained by mapping the AS topology. Each AS number approximately maps to an Internet service provider and its links are inter-ISP connections. A different representation of the Internet is obtained by mapping the AS topology. Each AS number approximately maps to an Internet service provider and its links are inter-ISP connections.

4. Connectivity distribution: probability P(k) that a given node has k links to other nodes. Connectivity distribution: probability P(k) that a given node has k links to other nodes.

6. Exponential network: highway network, power grid, proteins� conformation space, neural network of C elegans Scale-free network: WWW, internet, movie actors, coauthorship network, phone calls, metabolic networks, PIN, bank systems, world-airline network. Power law formula -> gamma connectivity exponent. For real systems, Gamma is scattered between 2 and 3.Exponential network: highway network, power grid, proteins� conformation space, neural network of C elegans Scale-free network: WWW, internet, movie actors, coauthorship network, phone calls, metabolic networks, PIN, bank systems, world-airline network. Power law formula -> gamma connectivity exponent. For real systems, Gamma is scattered between 2 and 3.

12. � each node has unit processing capability, but there is no restriction on the maximum amount of loads carried by the edges. - nodes have boundless processing capability, but there is a finite bandwidth associated to edges, which is the same for all edges When the loads are balanced, the transport capacity reaches its maximal value. How many current units can the network deliver without becoming congested? The network becomes congested as soon as there is a node for which this condition does not hold up and that node will be the one with the highest load. The network efficiency is solely dependent on the maximum load. When there is a finite bandwidth associated to the edges and the processing capability of nodes is unbounded reaches its maximum for a slightly positive beta value.� each node has unit processing capability, but there is no restriction on the maximum amount of loads carried by the edges. - nodes have boundless processing capability, but there is a finite bandwidth associated to edges, which is the same for all edges When the loads are balanced, the transport capacity reaches its maximal value. How many current units can the network deliver without becoming congested? The network becomes congested as soon as there is a node for which this condition does not hold up and that node will be the one with the highest load. The network efficiency is solely dependent on the maximum load. When there is a finite bandwidth associated to the edges and the processing capability of nodes is unbounded reaches its maximum for a slightly positive beta value.