We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study the model in its annealed random graph version, on a fixed...

We consider a finite set S={x1,…,xr} and associate to each element xi a probability pi. We then form sequences (N-strings) by drawing at random N elements from S with respect to the probabilities assigned to them. Each N-string generates a network where the elements of S are represented as...

We have studied the directed and weighted network in which the wards of London are vertices and two vertices are connected whenever there is at least one person commuting to work from one ward to another. Remarkably the in-strength and in-degree distribution tail is a power law with exponent...

We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either: (i) with probability p an incoming agent joins an existing group, or (ii) with probability 1−p...

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m “ambassador”...

We introduce a growing network model which generates both modular and hierarchical structure in a self-organized way. To this end, we modify the Barabási–Albert model into the one evolving under the principles of division and independence as well as growth and preferential attachment (PA). A...