Pengaruh hotspots dalam jaringan small world dan jaringan scale-free = Hotspots influence in small world and scale-free network

Cahayadi, Denny (2013) Pengaruh hotspots dalam jaringan small world dan jaringan scale-free = Hotspots influence in small world and scale-free network. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Small world network and scale-free network have important role in modeling complex network. Both of them have sucessfully described most of dynamic network in our life. Small world network and scale-free network can simply be identified by their unique parameters, such as average path length, clustering coefficient, and degree of distribution. The purpose of this work is to observe the relationship between hotspots and the behavior of small world and scale-free network. The simulation will re-create small world Watts-Strogatz model and scale-free Barabasi-Albert model. Small world simulation shows that in low randomness (0,01<p<0,03), the average path length increases drastically with increasing number of isolated nodes. In moderate randomness (between 0,04 and 0,05), the increase of average path length tends to be linear with a low slope. The linearity behavior with lower slope appears in the high randomness (above 0,05). This linearity also appears in effect of isolating hotspots in scale-free network. Simulation also shows that in small world network, isolating hotspots causes the increase of clustering coefficient, altough it is not significant and tends to be stable. In contrast, in scale-free network, isolating hotspots causes a drop in clustering coefficient, although the starting clustering coefficient itself is already low./ Small world dan jaringan scale-free memiliki peran yang penting dalam pemodelan jaringan kompleks. Keduanya berhasil menggambarkan banyak jaringan dalam kehidupan sehari-hari. Jaringan small world dan jaringan scalefree mudah teridentifikasi melalui parameternya yang unik, yaitu average path length, koefisien clustering dan degree distribution. Tujuan penyusunan makalah ini adalah untuk mengamati hubungan antara hotspots dengan perilaku jaringan small world dan jaringan scale-free. Simulasi dilakukan dengan membentuk ulang model small world Watts-Strogatz dan model scale-free Barabasi-Albert. Hasil simulasi small world menunjukkan bahwa pada randomness antara 0,01 sampai 0,03, average path length jaringan akan meningkat secara drastis seiring dengan banyaknya jumlah hotspots yang diisolasi. Sedangkan, pada randomness diantara 0,03 sampai 0,05, kenaikan average path length akibat isolasi hotspots cenderung linear dengan slope yang rendah. Linearitas dengan slope yang lebih rendah lagi terlihat pada efek isolasi terhadap average path length pada randomness diatas 0,05. Linearitas dengan slope rendah juga tampak pada efek isolasi hotspots terhadap average path length pada scale-free network. Hasil simulasi juga menunjukkan bahwa pada jaringan small world, isolasi hotspots akan meningkatkan koefisien clustering jaringan. Namun, kenaikan tersebut tidak signifikan dan cederung stabil. Hal yang berbeda tampak pada efek isolasi terhadap koefisien clustering pada jaringan scale-free Barabasi-Albert. Isolasi hotspots akan menurunkan koefisien clustering jaringan, meskipun koefisien clustering mula-mula pada jaringan Barabasi-Albert memang sudah rendah.

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