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Register a new userScale-dependent measure of network centrality from diffusion dynamics
قياس معيار المركزية للشبكة معتمد على الديناميكا الانتشارية
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تقييمات الكلاسيكية لوسطية الرسم البياني تلتقط جوانب مختلفة من أهمية العقد، من المحلي (مثل الدرجة) إلى العالمي (مثل القرب). هنا نستغل الاتصال بين الانتشار والهندسة لإدخال قياس متعدد المقاييس للوسطية. يُعرف العقد بأنه وسطي إذا كان يقطع المتوسطية للانتشار نتيجة للحدود الفعالة والغيورية في الرسم البياني. يكون قياسنا طبيعيًا متعدد المقاييس، لأنه يحسب بالنسبة لاحياء الرسم البياني ضمن الإطار الزمني المتغير للانتشار. ونجد أن وسطية العقد يمكن أن تختلف بشكل كبير في مقاييس مختلفة. على وجه الخصوص، يتطابق قياسنا مع الدرجة (أي المحور) في المقاييس الصغيرة ومع القرب (أي الجسور) في المقاييس الكبيرة، ويكشف أيضًا عن وجود هياكل متعددة المركزية في الشبكات المعقدة. من خلال فحص الوسطية عبر المقاييس، يوفر قياسنا تقييمًا لأهمية العقد بالنسبة للعمليات المحلية والعالمية في الشبكة.
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale centrality measure. A node is defined to be central if it breaks the metricity of the diffusion as a consequence of the effective boundaries and inhomogeneities in the graph. Our measure is naturally multiscale, as it is computed relative to graph neighbourhoods within the varying time horizon of the diffusion. We find that the centrality of nodes can differ widely at different scales. In particular, our measure correlates with degree (i.e., hubs) at small scales and with closeness (i.e., bridges) at large scales, and also reveals the existence of multi-centric structures in complex networks. By examining centrality across scales, our measure thus provides an evaluation of node importance relative to local and global processes on the network.
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Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on Stauffer-Hohnisch-Pittnauer (SHP) networks. To control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the critical noise $q_{c}$ to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.
We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counter-intuitive effects on information diffusion when social reinforcement is present. We show that strong communities can facilitate global diffusion by enhancing local, intra-community spreading. Using both analytic approaches and numerical simulations, we demonstrate the existence of an optimal network modularity, where global diffusion require the minimal number of early adopters.
The rapid diffusion of information and the adoption of social behaviors are of critical importance in situations as diverse as collective actions, pandemic prevention, or advertising and marketing. Although the dynamics of large cascades have been extensively studied in various contexts, few have systematically examined the impact of network topology on the efficiency of information diffusion. Here, by employing the linear threshold model on networks with communities, we demonstrate that a prominent network feature---the modular structure---strongly affects the speed of information diffusion in complex contagion. Our simulations show that there always exists an optimal network modularity for the most efficient spreading process. Beyond this critical value, either a stronger or a weaker modular structure actually hinders the diffusion speed. These results are confirmed by an analytical approximation. We further demonstrate that the optimal modularity varies with both the seed size and the target cascade size, and is ultimately dependent on the network under investigation. We underscore the importance of our findings in applications from marketing to epidemiology, from neuroscience to engineering, where the understanding of the structural design of complex systems focuses on the efficiency of information propagation.
There are different measures to classify a networks data set that, depending on the problem, have different success. For example, the resistance distance and eigenvector centrality measures have been successful in revealing ecological pathways and differentiating between biomedical images of patients with Alzheimers disease, respectively. The resistance distance measures the effective distance between any two nodes of a network taking into account all possible shortest paths between them and the eigenvector centrality measures the relative importance of each node in the network. However, both measures require knowing the networks eigenvalues and eigenvectors -- eigenvectors being the more computationally demanding task. Here, we show that we can closely approximate these two measures using only the eigenvalue spectra, where we illustrate this by experimenting on elemental resistor circuits and paradigmatic network models -- random and small-world networks. Our results are supported by analytical derivations, showing that the eigenvector centrality can be perfectly matched in all cases whilst the resistance distance can be closely approximated. Our underlying approach is based on the work by Denton, Parke, Tao, and Zhang [arXiv:1908.03795 (2019)], which is unrestricted to these topological measures and can be applied to most problems requiring the calculation of eigenvectors.
We study the lobby index (l-index for short) as a local node centrality measure for complex networks. The l-inde is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of biological network (Yeast interaction protein-protein network) and a linguistic network (Moby Thesaurus II). In both networks, the l-index has poor correlation with betweenness but correlates with degree and Eigenvector. Being a local measure, one can take advantage by using the l-index because it carries more information about its neighbors when compared with degree centrality, indeed it requires less time to compute when compared with Eigenvector centrality. Results suggests that l-index produces better results than degree and Eigenvector measures for ranking purposes, becoming suitable as a tool to perform this task.
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