Persistence of information flow: a multiscale characterization of human brain
B. Benigni, A. Ghavasieh, A. Corso, V. d'Andrea, M. De Domenico, Network Neuroscience 5, 831 (2021) Abstract » Read » BibTeX Persistence of information flow: a multiscale characterization of human brainInformation exchange in the human brain is crucial for vital tasks and to drive diseases. Neuroimaging techniques allow for the indirect measurement of information flows among brain areas and, consequently, for reconstructing connectomes analyzed through the lens of network science. However, standard analyses usually focus on a small set of network indicators and their joint probability distribution. Here, we propose an informationtheoretic approach for the analysis of synthetic brain networks (based on generative models) and empirical brain networks, and to assess connectome's information capacity at different stages of dementia. Remarkably, our framework accounts for the whole network state, overcoming limitations due to limited sets of descriptors, and is used to probe human connectomes at different scales. We find that the spectral entropy of empirical data lies between two generative models, indicating an interpolation between modular and geometrydriven structural features. In fact, we show that the mesoscale is suitable for characterizing the differences between brain networks and their generative models. Finally, from the analysis of connectomes obtained from healthy and unhealthy subjects, we demonstrate that significant differences between healthy individuals and the ones affected by Alzheimer’s disease arise at the microscale (max. posterior probability smaller than 1%) and at the mesoscale (max. posterior probability smaller than 10%). 

Quantifying efficient information exchange in real network flows
G. Bertagnolli, R. Gallotti, M. De Domenico, Communications Physics 4, 125 (2021) Abstract » Read » BibTeX Quantifying efficient information exchange in real network flowsNetwork science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and network flows. It is wellknown that the topology of a network affects its resilience to failures or attacks, as well as its functions. Many real systems—such as the Internet, transportation networks and the brain—exchange information, so it is crucial to quantify how efficiently system’s units communicate. Measures of parallel communication efficiency for weighted networks rely on the identification of an ideal version of the system, which currently lacks a universal definition. Consequently, an inattentive choice might hinder a rigorous comparison of network flows across scales or might lead to a descriptor not robust to fluctuations in the topology or the flows. We propose a physicallygrounded estimator of flow efficiency valid for any weighted network, regardless of scale, nature of weights and (missing) metadata, allowing for comparison across disparate systems. Our estimator captures the effect of flows heterogeneity along with topological differences of both synthetic and empirical systems. We also show that cutting the heaviest connections may increase the average efficiency of the system and hence, counterintuively, a sparser network is not necessarily less efficient. 

Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models
P. Tewarie et al, New Journal of Physics 23, 063065 (2021) Abstract » Read » BibTeX Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator modelsLargescale neurophysiological networks are often reconstructed from bandpass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can be significant coupling between frequency bands (interlayer connectivity). A multilayer network approach offers a solution to analyze frequencyspecific networks in one framework. We propose to use a recently developed network reconstruction method in conjunction with phase oscillator models to estimate interlayer connectivity that optimally fits the empirical data. This approach determines interlayer connectivity based on observed frequencyspecific time series of the phase and a connectome derived from diffusion weighted imaging. The performance of this interlayer reconstruction method was evaluated insilico. Our reconstruction of the underlying interlayer connectivity agreed to very high degree with the ground truth. Subsequently, we applied our method to empirical restingstate MEG data obtained from healthy subjects and reconstructed twolayered networks consisting of either alphatobeta or thetatogamma band connectivity. Our analysis revealed that interlayer connectivity is dominated by a multiplex structure, i.e. by onetoone interactions for both alphatobeta band and thetatogamma band networks. For theta–gamma band networks, we also found a plenitude of interlayer connections between distant nodes, though weaker connectivity relative to the onetoone connections. Our work is an stepping stone towards the identification of interdependencies across frequencyspecific networks. Our results lay the ground for the use of the promising multilayer framework in this field with moreinformed and justified interlayer connections. 

Network Geometry
M. Boguna, I. Bonamassa, M. De Domenico, S. Havlin, D. Krioukov, M.A. Serrano, Nature Reviews Physics 3, 114 (2021) Abstract » Read » BibTeX Network GeometryNetworks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, selfsimilarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity. 

Multilayer connector hub mapping reveals key brain regions supporting expressive language
B. Williamson, M. De Domenico, D. Kadis, Brain Connectivity 11, 45 (2020) Abstract » Read » BibTeX Multilayer connector hub mapping reveals key brain regions supporting expressive languageHow components of the distributed brain networks that support cognition participate in typical functioning remains a largely unanswered question. An important subgroup of regions in the larger network are connector hubs, which are areas that are highly connected to several other functionallyspecialized sets of regions, and are likely important for sensorimotor integration. The present study attempts to characterize connector hubs involved in typical expressive language functioning using a datadriven, multimodal, full multilayer MEG connectivitybased pipeline. Twelve adolescents, 1618 years of age (5 male) participated in this study. Participants underwent MEG scanning during a verb generation task. MEG and structural connectivity were calculated at the wholebrain level. Amplitudeamplitude coupling (AAC) was used to compute functional connections both within and between discrete frequency bins. AAC values were then multiplied by a binary structural connectivity matrix, then entered into full multilayer network analysis. Initially, hubs were defined based on multilayer versatility and subsequently reranked by a novel measure called delta centrality on interconnectedness (DCI). DCI is defined as the percent change in interfrequency interconnectedness after removal of a hub. We resolved regions that are important for betweenfrequency communication among other areas during expressive language, with several potential theoretical and clinical applications that can be generalized to other cognitive domains. Our multilayer, datadriven framework captures nonlinear connections that span across scales that are often missed in conventional analyses. The present study suggests that crucial hubs may be conduits for interfrequency communication between action and perception systems that are crucial for typical functioning. 

Statistical physics of complex information dynamics
A. Ghavasieh, C. Nicolini, M. De Domenico, Phys. Rev. E 102, 052304 (2020) Abstract » Read » BibTeX Statistical physics of complex information dynamicsThe constituents of a complex system exchange information to function properly. Their signaling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange has been widely modeled by means of distinct spreading processes—such as continuoustime diffusion, random walks, synchronization and consensus—on top of complex networks, a unified and physically grounded framework to study information dynamics and gain insights about the macroscopic effects of microscopic interactions is still eluding us. In this paper, we present this framework in terms of a statistical field theory of information dynamics, unifying a range of dynamical processes governing the evolution of information on top of static or timevarying structures. We show that information operators form a meaningful statistical ensemble and their superposition defines a density matrix that can be used for the analysis of complex dynamics. As a direct application, we show that the von Neumann entropy of the ensemble can be a measure of the functional diversity of complex systems, defined in terms of the functional differentiation of higherorder interactions among their components. Our results suggest that modularity and hierarchy, two key features of empirical complex systems—from the human brain to social and urban networks—play a key role to guarantee functional diversity and, consequently, are favored. 

Enhancing transport properties in interconnected systems without altering their structure
A. Ghavasieh, M. De Domenico, Phys. Rev. Research 2, 013155 (2020) Abstract » Read » BibTeX Enhancing transport properties in interconnected systems without altering their structureUnits of complex systems  such as neurons in the brain or individuals in societies  must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas in the human brain, or allowing for fast navigation of humans and goods in complex transportation landscapes. The coexistence of different types of relationships among the units, entailing a multilayer represention in which types are considered as networks encoded by layers, plays an important role in the quality of information exchange among them. While altering the structure of such systems  e.g., by physically adding (or removing) units, connections or layers  might be costly, coupling the dynamics of subset(s) of layers in a way that reduces the number of redundant diffusion pathways across the multilayer system, can potentially accelerate the overall information flow. To this aim, we introduce a framework for functional reducibility which allow us to enhance transport phenomena in multilayer systems by coupling layers together with respect to dynamics rather than structure. Mathematically, the optimal configuration is obtained by maximizing the deviation of system's entropy from the limit of free and noninteracting layers. Our results provide a transparent procedure to reduce diffusion time and optimize noncompact search processes in empirical multilayer systems, without the cost of altering the underlying structure. 

Multilayer network modeling of integrated biological systems
M. De Domenico, Physics of Life Reviews 24, 149152 (2018) Abstract » Read » BibTeX Multilayer network modeling of integrated biological systemsBiological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several studies are highlighting how simple networks – obtained by aggregating or neglecting temporal or categorical description of biological data – are not able to account for the richness of information characterizing biological systems. More complex models, namely multilayer networks, are needed to account for interdependencies, often varying across time, of biological interacting units within a cell, a tissue or parts of an organism. Gosak et al. [1] review the most recent advances in the application of multilayer networks for modeling complex biological systems, from molecular interactions within a cell to neuronal connectivity of the human brain. 

Diffusion Geometry Unravels the Emergence of Functional Clusters in Collective Phenomena
M. De Domenico, Phys. Rev. Lett. 118, 168301 (2017) Abstract » Read » BibTeX Diffusion Geometry Unravels the Emergence of Functional Clusters in Collective PhenomenaCollective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from topological ones. In biological systems, like the human brain, the overall functionality is often favored by the interplay between connectivity and synchronization dynamics, with functional clusters that do not coincide with anatomical modules in most cases. In social, sociotechnical, and engineering systems, the quest for consensus favors the emergence of clusters. Despite the unquestionable evidence for mesoscale organization of many complex systems and the heterogeneity of their interconnectivity, a way to predict and identify the emergence of functional modules in collective phenomena continues to elude us. Here, we propose an approach based on random walk dynamics to define the diffusion distance between any pair of units in a networked system. Such a metric allows us to exploit the underlying diffusion geometry to provide a unifying framework for the intimate relationship between metastable synchronization, consensus, and random search dynamics in complex networks, pinpointing the functional mesoscale organization of synthetic and biological systems. 

Multilayer modeling and analysis of human brain networks
M. De Domenico, GigaScience 6, 18 (2017) Abstract » Read » BibTeX Multilayer modeling and analysis of human brain networksUnderstanding how the human brain is structured, and how its architecture is related to the function, is of paramount importance for a variety of applications, including, but not limited to, new ways to prevent, deal with and cure brain diseases, such as Alzheimer’s or Parkinson’s, and psychiatric disorders, such as Schizophrenia. The recent advances in structural and functional neuroimaging, together with the increasing attitude to interdisciplinary approaches involving computer science, mathematics and physics, are fostering interesting results from computational neuroscience, that are quite often based on the analysis of complex network representation of human brain. In the last years, this representation experienced a theoretical and computational revolution that are breaching neuroscience, allowing to cope with the increasing complexity of human brain across multiple scales and in multiple dimensions, and to model structural and functional connectivity from new perspectives, often combined with each other. In this work, we will review the main achievements obtained from interdisciplinary research based on magnetic resonance imaging and establishing, de facto, the birth of multilayer network analysis and modeling of human brain. 

Researcher incentives: EU cash goes to the sticky and attractive
M. De Domenico, A. Arenas, Nature 531, 580 (2016) Abstract » Read » BibTeX Researcher incentives: EU cash goes to the sticky and attractiveWe find that winning European research money (Nature 530, 33; 2016) is, among other things, contingent on how well national governments manage to retain their own scientists and to attract others from abroad. We analysed statistical indicators of scientists' mobility in the European Union for 200714 (erc.europa.eu and go.nature.com/bpeylu) to determine the 'attractiveness' of different countries to scientists from abroad, as well as their 'stickiness' in preventing native researchers from moving away (known as brain drain). We quantified attractiveness and stickiness as the relative difference between incoming or remaining researchers, respectively, and outgoing ones. For both measures, we found that the higher the value, the better are that country's chances of securing European research funding. The United Kingdom and Sweden are high scorers in both; Italy is among the lowest (further details from M. de D. and A. A.; see go.nature.com/wyvtls). We conclude that there is a 'rich get richer' effect for countries that have high attractiveness and stickiness scores. Those nations also boast a high gross domestic product per capita, and tend to invest more in research and development. This means that they can lure and retain the best researchers by providing competitive salaries and a guaranteed future in research.  Full text 

Mapping multiplex hubs in human functional brain network
M. De Domenico, S. Sasai, A. Arenas, Frontiers in Neuroscience 10, 326 (2016) Abstract » Read » BibTeX Mapping multiplex hubs in human functional brain networkTypical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral interregional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network and face this challenge by exploiting the recent advances in the analysis of multiplex topologies. First, we show that each frequency band carries unique topological information, fundamental to accurately model brain functional networks. We then demonstrate that hubs in the multiplex network, in general different from those ones obtained after discarding or aggregating the measured signals as usual, provide a more accurate map of brain's most important functional regions, allowing to distinguish between healthy and schizophrenic populations better than conventional network approaches. 

MuxViz: a tool for multilayer analysis and visualization of networks
M. De Domenico, Mason A. Porter, A. Arenas, Journal of Complex Networks 3, 159 (2015) Abstract » Read » BibTeX MuxViz: a tool for multilayer analysis and visualization of networksMultilayer relationships among entities and information about entities must be accompanied by the means to analyse, visualize and obtain insights from such data. We present opensource software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyse and interactively visualize multilayer data using empirical genetic, neuronal and transportation networks. Our software is available at https://github.com/manlius/muxViz. 

Emergence of assortative mixing between clusters of cultured neurons
S. Teller, C. Granell, M. De Domenico, J. Soriano, S. Gomez, A. Arenas, PLOS Comput. Biol. 10(9), e1003796 (2014) Abstract » Read » BibTeX Emergence of assortative mixing between clusters of cultured neuronsThe analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to unravel the interplay between structure and functionality of neuronal systems. Here, we monitor the spontaneous selfsustained dynamics in neuronal cultures formed by interconnected aggregates of neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters in sequences termed bursts. The analysis of the time delays between clusters' activations within the bursts allows the reconstruction of the directed functional connectivity of the network. We propose a method to statistically infer this connectivity and analyze the resulting properties of the associated complex networks. Surprisingly enough, in contrast to what has been reported for many biological networks, the clustered neuronal cultures present assortative mixing connectivity values, meaning that there is a preference for clusters to link to other clusters that share similar functional connectivity, as well as a richclub core, which shapes a ‘connectivity backbone’ in the network. These results point out that the grouping of neurons and the assortative connectivity between clusters are intrinsic survival mechanisms of the culture. 
