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Mobile Communication Networks Vahid Mirjalili Department of Mechanical Engineering Department of Biochemistry & Molecular Biology

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Understanding Social Networks Examine the communication pattern of million mobile phone users Social networks are robust to the removal of strong ties, but fall apart if the weak ties are removed 18 weeks of all mobile call records, 90% of the population of the country use mobile phones A single call between 2 individuals during 18 weeks is ignored Reciprocal calls with long durations are considered as some type of relationship (family, leisure,..)

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Building the Mobile Call Graph (MCG) An undirected link between A & B if there is at least one reciprocal call between them The weights: A large number of single calls are removed The MCG: 84.1% of the graph belong to a single connected cluster (giant component) Time for sampling? – little difference between sampling 2- or 3-months

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MCG results: Degree distribution: Number of links per node Most of the people only interact with a few Only a few communicate with more than 10 people Fitted with exponential curve (strong decay)

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Link weight distribution: The majority only have short communication time A few have long conversations

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Overlap between 2 nodes: The overlap between two nodes: the ratio of their shared nodes to their total connected nodes

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3- hypothesses governing the social networks 1.Global Efficiency Principle – Complex networks organize themselves in a way that the tie strengths maximize the overall flow in the network – Correlation between the weight of a link and its betweenness centrality (the number of shortest paths of all pairs of nodes passing through it) 2.Dyadic hypothesis – The strength of a link only depends on the nature of the relationship between the individuals – Tie strength is independent of the network surrounding it 3.Strength of weak tie hypothesis – The strength of a tie between A and B increases as the overlap between their friendship circles increases

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The network around a randomly selected node (up to 6 levels) Link color shows tie strength Majority of strong ties are found within clusters (intra-cluster links vs. inter-cluster) Inter-community links are usually weaker

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In contract to a real network A dyadic network, generated by randomly permuting the ties in the previous one => dyadic hypothesis

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The weights are derived based on the links betweenness centrality The links connecting different communities have high (red) but the links inside a community have low (green)

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Tie strength & network structure Removing weak / strong ties: The size of giant component: – The fraction of nodes that can all reach other as a function of the fraction of removed links Network disintegration: – Based on ties strength: – Based on overlap:

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Removing links Based on weights Based on overlap Red: removing the weakest ties Black: removing the strongest ties

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Percolation theory: – divergence occurs as we approach the critical threshold – phase transition Removing the weak ties first, shows a divergence No divergence observed if removing the strong ties first

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Contrast between Social Networks vs Biological Networks Biological networks: strong ties play more important roles than weak ties Social networks: strong ties are inter- community links, and removing strong ties will disconnect the small communities from each other, but the global network will NOT collapse

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Information Diffusion Monitoring the information spread starting from a randomly selected individual with some novel information Probability of passing the information:

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For the control run, the average of all the weights is used Control : all ties are considered equal Real : considering the real network with real weights trapped Information gets trapped inside a community before leaving for a new community

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Distribution of the strength of a tie responsible for the first infection of a node Real network: peak at w=100 (intermediate strength) control: information spread is independent of tie strength (weak ties inside a community are responsible for the information spread)

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Overall direction of information flow Number of times information is passed in the given direction Total number of transmission from the link

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In the control runs, the information flows through the shortest paths In the real network: the information is passed through a strong tie backbone, and the regions connected to it – Half of the network is rarely affected (lower part of the real simulation)

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Conclusion: Unexpected result: removal of weak ties can collapse the social network, while other networks are mainly fragile to the removal if string ties Information trapping in small communities observed The information is mostly passed through intermediate ties

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