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# my current research about social netwerok

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## Meng Cai

on 6 May 2010

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#### Transcript of my current research about social netwerok

S personal attribute department organization work communication network social interaction network hindrance network Resignation discussion network superior expected netwrok skill development network individual performance group performance degree centrality
betweenness centrality
closeness centrality
Cohesive Subgroups Density
Degree Centrilization
Betweenness Centrilization
Small-world Phenomenon
Clustering Coefficient
Average path length random network
regular network
scale-free network
small-world network a new network structure entropy-finding “black swan” in network the importance of node network structure entropy the development of network structure entropy network & performance three attributes:
1. it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility.
11. it carries an extreme impact.
111. in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable. note: a.entropy varies when network size varies in regular network.(given degree distribution and density ) note: b.entropy varies when degree distribution varies .(given network size and density ) note: c.entropy varies when density varies in correspond random network or scale-free network.(given degree distribution and network size ) information misdirection random network scale-free network network connectivity (network size=500) density=0.004 density=0.036 density=0.02 density=0.1 density=0.9 increment=2 increment=10 increment=18 random network scale-free network with 20 initial nodes density=0.5 different finding Each curve line represents the evolution process of entropy with different increment.
The plane curves near top and bottom of the figure represent the probable maximum value(corresponding to regular network) and the minimum value(corresponding to star network ) respectively. Each curve line represents the evolution process of entropy with different density.
The entropy of random network increases quickly and reach to a stable value, which is near to the probable maximum value.
red curve: random network
blue curve: scale-free network The entropy of random network is greater than that of scale-free netork for any density, which means the latter is more heterogeneous.
There is the positive correlation between entropy and density when density is no bigger than 0.1.
The entropy of work communication network is bigger than that of social interaction network in most enterprises except BD, which means the distribution of power or importance is more equal and steady, and heterogeneity is less.
"note a b c" means the entropy can fully reflect the network structure under the combined action of the degree distribution, network density and network size.
The entropy value of real-network is less than correspondent scale-free network except social interaction network of YB, which means real-world network is not homogeneous, because scale-free network is highly heterogeneous with structure perspective.
network size=100;network density=0.2
black dotted line: the number of nodes in group in which the degree of member is not greater than distinction value.
red dotted line(overlap to red curve in a short time): the number of group in which the degree of member is greater than distinction value.
red curve: the number of nodes obtained information without misdirection.
black curve: the number of nodes obtained information in group in which the degree of member is not greater than distinction value.
green curve: the number of nodes obtained information in group in which the degree of mumber is greater than distinction value. network size=100; number of initial nodes=20;increment=10;
Lots of researchers and scholars had been studying on infectious disease spread, rumor diffusion and information propagation, which are very common and important in our real world. With the structure perspective , numerous important discoveries had been found. But previous studies are based on two basic assumptions: the information just spread in a certain group and has a definitive direction, that means the information always know whrer should it goes and it does.
But in our real-life,group classification is real exist: Some important information(future policy decision or financial details) just known by the members of the board in enterprise. Some diseases just spread in certain kind of people or certain species.
And misdirection is also real exist:information disclosure in enterprise or disease spread to other species as genetic changes.
So we abandoned previous assumptions to find the correlationship between propagation characteristic and network structure.

Network connectivity is very important for real-world networks,such as power grid and food web.
A fraction of the nodes and their connections are removed randomly or intentionally, the netwrok disintegrates into smaller,disconnected parts.Resilience of network to failures of nodes or to intentional attacks represents the network's robustness.
The most important finding in previous research is the emergent property , that means there is critical threshold value of the number of removed nodes.(Below that value, there still a connected cluster.)
But no one observes the connectivity of the removed nodes, which I am interested in.
As intentional attack usually choose the node with greater degree, I distinguish groups by degree.
most interesting findings:
emergent property both in two groups;
the overlap part between complete connected groups YZ-work network YZ-social network BD-work network BD-social network SL-work network SL-social network YB-work network YB-social network But the real-life networks show the different characteristics Why these findings are different? entropy is an important physical variable which describes the non-order of the system nodes connect each other randomly,and the degree distribution abide by bell-sharped. degree distribution with strict rule
nodes connect each other with perferential attatchment, and the connectivity distributions are in a power-law form that is independent of the network scale, which implies that nodes with only a few edges are numerous,but a few nodes have a very large number of edges. a network to describe the transition from a regular lattice to a random graph. some existing findings,such as community structure: YZ-work YZ-social BD-work BD-social SL-work SL-social YB-work YB-social finding the correlationship between social netwrok and department performance considering the interactions between formal network and informal netwrok
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