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Register a new userScaling Properties in Time-Varying Networks with Memory
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The formation of network structure is mainly influenced by an individual nodes activity and its memory, where activity can usually be interpreted as the individual inherent property and memory can be represented by the interaction strength between nodes. In our study, we define the activity through the appearance pattern in the time-aggregated network representation, and quantify the memory through the contact pattern of empirical temporal networks. To address the role of activity and memory in epidemics on time-varying networks, we propose temporal-pattern coarsening of activity-driven growing networks with memory. In particular, we focus on the relation between time-scale coarsening and spreading dynamics in the context of dynamic scaling and finite-size scaling. Finally, we discuss the universality issue of spreading dynamics on time-varying networks for various memory-causality tests.
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We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself, but the activity provided initially is sustained within the collective of interacting agents. In contrast to existing models of self-sustaining activity that are caused by (long) loops present in the network, here we focus on tree--like structures and examine activation mechanisms that are due to temporal memory of the nodes. This approach is motivated by applications in social media, where long network loops are rare or absent. Our results suggest that under a weak behavioral noise, the nodes robustly split into several clusters, with partial synchronization of nodes within each cluster. We also study the randomly-weighted version of the models where the nodes are allowed to change their connection strength (this can model attention redistribution), and show that it does facilitate the self-sustained activity.
The largest eigenvalue of a networks adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expression relating the value of the largest eigenvalue of a given network to the largest eigenvalue of two network subgraphs, considered as isolated: The hub with its immediate neighbors and the densely connected set of nodes with maximum $K$-core index. We validate this formula showing that it predicts with good accuracy the largest eigenvalue of a large set of synthetic and real-world topologies. We also present evidence of the consequences of these findings for broad classes of dynamics taking place on the networks. As a byproduct, we reveal that the spectral properties of heterogeneous networks built according to the linear preferential attachment model are qualitatively different from those of their static counterparts.
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the networks adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since these degeneracies are rarely observed in model graphs, we present results for various cancer networks. This approach gives an opportunity to search for structures contributing to degeneracy which might have an important role in a network.
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a systems unitary components and its emergent synchronized functioning. An increased number of setups from the real world found therefore a representation in term of graphs, while more and more sophisticated methods were developed with the aim of furnishing a realistic description of the connectivity patterns under study. In particular, a significant number of systems in physics, biology and social science features a time-varying nature of the interactions among their units. We here give a comprehensive review of the major results obtained by contemporary studies on the emergence of synchronization in time-varying networks. In particular, two paradigmatic frameworks will be described in details. The first encompasses those systems where the time dependence of the nodes connections is due to adaptation, external forces, or any other process affecting each of the links of the network. The second framework, instead, corresponds to the case in which the structural evolution of the graph is due to the movement of the nodes, or agents, in physical spaces and to the fact that interactions may be ruled by space-dependent laws in a way that connections are continuously switched on and off in the course of the time. Finally, our report ends with a short discussion on promising directions and open problems for future studies.
The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network [1]; or, if immunized, would prevent the diffusion of a large scale epidemic [2,3]. Localizing this optimal, i.e. minimal, set of structural nodes, called influencers, is one of the most important problems in network science [4,5]. Despite the vast use of heuristic strategies to identify influential spreaders [6-14], the problem remains unsolved. Here, we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix [15] of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly-connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. Eventually, the present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase [16].
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