اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدقياس معيار المركزية للشبكة معتمد على الديناميكا الانتشارية
Scale-dependent measure of network centrality from diffusion dynamics
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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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