Hussein was last spotted kissing a baby in Baghdad in April 2003, and then his trace went cold.
Designed a deck of cards, each card engraved with the images of the 55 most wanted.
shows the strong predictive power of networks.
underlies the need to obtain accurate maps of the networks we aim to study; and the often heroic difficulties we encounter during the mapping process.
demonstrates the remarkable stability of these networks: The capture of Hussein was not based on fresh intelligence, but rather on his pre-invasion social links, unearthed from old photos stacked in his family album.
shows that the choice of network we focus on makes a huge difference: the hierarchical tree, that captured the official organization of the Iraqi government, was of no use when it came to Saddam Hussein's whereabouts.
An important theme of this class:
we must understand how network structure affects the robustness of a complex system.
develop quantitative tools to assess the interplay between network structure and the dynamical processes on the networks, and their impact on failures.
We will learn that failures reality failures follow reproducible laws, that can be quantified and even predicted using the tools of network science.
[adj., v. kuh m-pleks, kom-pleks; n. kom-pleks] –adjective
Source: Dictionary.coma scientific theory which asserts that some systems display behavioral phenomena that are completely inexplicable by any conventional analysis of the systems’ constituent parts. These phenomena, commonly referred to as emergent behaviour, seem to occur in many complex systems involving living organisms, such as a stock market or the human brain. Source: John L. Casti, Encyclopædia Britannica
While the study of networks has a long history from graph theory to sociology, the modern chapter of network science emerged only during the first decade of the 21st century, following the publication of two seminal papers in 1998 and 1999.
The explosive interest in network science is well documented by the citation pattern of two classic network papers, the 1959 paper by Paul Erdos and Alfréd Rényi that marks the beginning of the study of random networks in graph theory [4] and the 1973 paper by Mark Granovetter, the most cited social network paper [5].
Both papers were hardly or only moderately cited before 2000. The explosive growth of citations to these papers in the 21st century documents the emergence of network science, drawing a new, interdisciplinary audience to these classic publications.
The human genome project, completed in 2001, offered the first comprehensive list of all human genes.
Terrorism is one of the maladies of the 21st century, absorbing significant resources to combat it worldwide.
While the H1N1 pandemic was not as devastating as it was feared at the beginning of the outbreak in 2009, it gained a special role in the history of epidemics: it was the first pandemic whose course and time evolution was accurately predicted months before the pandemic reached its peak.
In January 2010 network science tools have predicted the conditions necessary for the emergence of viruses spreading through mobile phones.
- The first major mobile epidemic outbreak that started in the fall of 2010 in China, infecting over 300,000 phones each day, closely followed the predicted scenario. The human brain, consisting of hundreds of billions of interlinked neurons, is one of the least understood networks from the perspective of network science.
The reason is simple:
Driven by the potential impact of such maps, in 2010 the National Institutes of Health has initiated the Connectome project, aimed at developing the technologies that could provide an accurate neuron-level map of mammalian brains.
Can one walk across the seven bridges and never cross the same bridge twice and get back to the starting place?
network often refers to real systems
Language: (Network, node, link)
graph: mathematical representation of a network
Language: (Graph, vertex, edge)
The choice of the proper network representation determines our ability to use network theory successfully.
In some cases there is a unique, unambiguous representation. In other cases, the representation is by no means unique. For example, the way we assign the links between a group of individuals will determine the nature of the question we can study.
If you connect individuals that work with each other, you will explore the professional network.
If you connect those that have a romantic and sexual relationship, you will be exploring the sexual networks.
In [174]:
%matplotlib inline
import matplotlib.pyplot as plt
import networkx as nx
Gu = nx.Graph()
for i, j in [(1, 2), (1, 4), (4, 2), (4, 3)]:
Gu.add_edge(i,j)
nx.draw(Gu, with_labels = True)
In [173]:
import networkx as nx
Gd = nx.DiGraph()
for i, j in [(1, 2), (1, 4), (4, 2), (4, 3)]:
Gd.add_edge(i,j)
nx.draw(Gd, with_labels = True)
In [175]:
nx.draw(Gu, with_labels = True)
In [177]:
nx.draw(Gd, with_labels = True)
In [20]:
import numpy as np
x = [1, 1, 1, 2, 2, 3]
np.mean(x), np.sum(x), np.std(x)
Out[20]:
In [22]:
plt.hist(x)
plt.show()
In [113]:
from collections import defaultdict, Counter
freq = defaultdict(int)
for i in x:
freq[i] +=1
freq
Out[113]:
In [37]:
freq_sum = np.sum(freq.values())
freq_sum
Out[37]:
In [38]:
px = [float(i)/freq_sum for i in freq.values()]
px
Out[38]:
In [41]:
plt.plot(freq.keys(), px, 'r-o')
plt.show()
In [182]:
plt.figure(1)
plt.subplot(121)
pos = nx.spring_layout(Gu) #定义一个布局，此处采用了spring布局方式
nx.draw(Gu, pos, with_labels = True)
plt.subplot(122)
nx.draw(Gd, pos, with_labels = True)
bipartite graph (or bigraph) is a graph whose nodes can be divided into two disjoint sets U and V such that every link connects a node in U to one in V; that is, U and V are independent sets.
has a path from each node to every other node and vice versa (e.g. AB path and BA path).
it is connected if we disregard the edge directions.
Strongly connected components can be identified, but not every node is partof a nontrivial strongly connected component.
In [215]:
G1 = nx.complete_graph(4)
pos = nx.spring_layout(G1) #定义一个布局，此处采用了spring布局方式
nx.draw(G1, pos = pos, with_labels = True)
In [206]:
print(nx.transitivity(G1))
In [216]:
G2 = nx.Graph()
for i, j in [(1, 2), (1, 3), (1, 0), (3, 0)]:
G2.add_edge(i,j)
nx.draw(G2,pos = pos, with_labels = True)
In [198]:
print(nx.transitivity(G2))
In [219]:
G3 = nx.Graph()
for i, j in [(1, 2), (1, 3), (1, 0)]:
G3.add_edge(i,j)
nx.draw(G3, pos =pos, with_labels = True)
In [200]:
print(nx.transitivity(G3))
THREE CENTRAL QUANTITIES IN NETWORK SCIENCE
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