Narrow Results

We propose a simple preferential attachment model of growing network using the complementary probability of Barabási–Albert (BA) model, i.e. $\mathrm{\Pi }(k_i)\propto 1-\frac{k_i}{{\sum }_j{k}_j}$. In this network, new nodes are preferentially attached to not well connected nodes. Numerical simulations, in perfect agreement with the master equation solution, give an exponential degree distribution. This suggests that the power law degree distribution is a consequence of preferential attachment probability together with “rich get richer” phenomena. We also calculate the average degree of a target node at time t$(〈k_s(t)〉)$ and its fluctuations, to have a better view of the microscopic evolution of the network, and we also compare the results with BA model.

In this paper, a new model of evolving networks is proposed based on the dynamical behaviors of nodes in the network. The probability that an existing node in the current network receives a new link from the newly added node is proportional to the defined "activity" of that particular node, which is equivalent to the energy signal of the system from a control theory point of view. This network is found to have the scale-free feature with the degree distribution in a power-law form. This model provides another explanation for the emergence of scale-free networks in many real-world examples.

We introduce and study a toy model which mimics the structure formation of a typical weighted network in the real world. In particular, the organizational structures of our networks are found to be consistent with real-world networks.

Considering the retarding effect of natural resources, environmental conditions, and other factors on network growth, the capacity of network nodes to connect to new edges is generally limited. Inspired by this hindered growth of many real-world networks, two types of evolving network models are suggested with different logistic growth schemes. In the global and local logistic network, the total number of network edges and the number of edges added into the network at each step are in line with the Logistic growth, respectively. The most exciting feature of the Logistic growth network is that the growth rule of network edges is first fast, then slow and finally reaches the saturation value $L$. Theoretical analysis and numerical simulation reveal that the node degrees of two new networks converge to the same results of the BA scale-free network, $a{(t/t_i)}^{1/2}$, as the growth rate $r$ approaches to 0. The local logistic network follows a bilateral power-law degree distribution with a given value of $r$. Meanwhile, for these two networks, it is found that the greater $r$ and $L$, the smaller the average shortest paths, the greater the clustering coefficients, and the weaker the disassortativity. Additionally, compared to the local logistic growth network, the clustering feature of the global logistic network is more obvious.

Axelrod's model describes the dissemination of a set of cultural traits in a society constituted by individual agents. In a social context, nevertheless, individual choices toward a specific attitude are also at the basis of the formation of communities, groups and parties. The membership in a group changes completely the behavior of single agents who start acting according to a social identity. Groups act and interact among them as single entities, but still conserve an internal dynamics. We show that, under certain conditions of social dynamics, the introduction of group dynamics in a cultural dissemination process avoids the flattening of the culture into a single entity and preserves the multiplicity of cultural attitudes. We also consider diffusion processes on this dynamical background, showing the conditions under which information as well as innovation can spread through the population in a scenario where the groups' choices determine the social structure.