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We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…
Recent research on deep graph learning has shifted from static to dynamic graphs, motivated by the evolving behaviors observed in complex real-world systems. However, the temporal extension in dynamic graphs poses significant data…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
We present a general computational theory of stem cell networks and their developmental dynamics. Stem cell networks are special cases of developmental control networks. Our theory generates a natural classification of all possible stem…
We address the problem of social network de-anonymization when relationships between people are described by scale-free graphs. In particular, we propose a rigorous, asymptotic mathematical analysis of the network de-anonymization problem…
We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are…
We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a…
A Chain Event Graph (CEG) is a graphial model which designed to embody conditional independencies in problems whose state spaces are highly asymmetric and do not admit a natural product structure. In this paer we present a probability…
Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static…
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are…
Memory is an important cognitive function for humans. How a brain with such a small power can complete such a complex memory function, the working mechanism behind this is undoubtedly fascinating. Engram theory views memory as the…
Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC threshold…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome…
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical…