Stochastic Process-based Method for Degree-Degree Correlation of Evolving Networks

We introduce a stochastic model of growing networks where both, the number of new nodes which joins the network and the number of connections, vary stochastically. We provide an exact mapping between this model and zero range process, and use this mapping to derive an analytical solution of degree distribution for any given evolution rule. One can also use this mapping to infer about a possible evolution rule for a given network. We demonstrate this for protein-protein intera...

Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-deletion and vulnerability to targeted node-deletion have concentrated only on power-law degree distribution and ignored degree correlation. This study looks specifically at the effect degree-correlation has on robustness and vulnerability in scale-free networks. Our results confirm Newman's finding...

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defi...

We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully describe long-range degree correlations with respect to $k$ and $k'$ of two nodes and shortest path length $l$ between them. We present general relations among these probabilities and clarify the relevance to nearest-neighbor degree correla...

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here, we use scaling theory to quantify the degree of correlations in the particular case of networks with a power-law degree distribution. These networks are classified in terms of their correlation properties, revealing additional information o...

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, beca...

Many real-world networks exhibit degree-degree correlations between nodes separated by more than one step. Such long-range degree correlations (LRDCs) can be fully described by one joint and four conditional probability distributions with respect to degrees of two randomly chosen nodes and shortest path distance between them. While LRDCs are induced by nearest-neighbor degree correlations (NNDCs) between adjacent nodes, some networks possess intrinsic LRDCs which cannot be ge...

The evolution processes of complex systems carry key information in the systems' functional properties. Applying machine learning algorithms, we demonstrate that the historical formation process of various networked complex systems can be extracted, including protein-protein interaction, ecology, and social network systems. The recovered evolution process has demonstrations of immense scientific values, such as interpreting the evolution of protein-protein interaction network...

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and non-linearities which can be present in real-world networks. The model generates weighted graphs exhibiting ...

For any initial correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations. We find that it is possible to turn an initi...