By Guanrong Chen, Xiaofan Wang, Xiang Li
Complicated networks comparable to the web, WWW, transportation networks, strength grids, organic neural networks, and medical cooperation networks of all types offer demanding situations for destiny technological development.
• the 1st systematic presentation of dynamical evolving networks, with many updated functions and homework tasks to augment study
• The authors are all very lively and famous within the quickly evolving box of advanced networks
• advanced networks have gotten an more and more very important sector of research
• offered in a logical, confident sort, from easy via to advanced, studying algorithms, via to build networks and examine demanding situations of the long run
Read Online or Download Fundamentals of complex networks : models, structures, and dynamics PDF
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Fundamentals of complex networks : models, structures, and dynamics
Complicated networks corresponding to the net, WWW, transportation networks, strength grids, organic neural networks, and clinical cooperation networks of all types offer demanding situations for destiny technological improvement. • the 1st systematic presentation of dynamical evolving networks, with many up to date functions and homework tasks to augment research• The authors are all very energetic and recognized within the speedily evolving box of advanced networks• advanced networks have gotten an more and more very important zone of study• awarded in a logical, positive kind, from uncomplicated via to complicated, reading algorithms, via to build networks and learn demanding situations of the longer term
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Additional info for Fundamentals of complex networks : models, structures, and dynamics
Example text
This can reveal the hierarchical structure of a graph, where higher cores and higher-coreness nodes belong to higher-levels of the hierarchical graph. Clearly, the star-shaped and ring-shaped graphs do not have prominent hierarchical structures. The main implication of the concept of coreness, on the other hand, is that a graph with a higher coreness will have better robustness against intentional attacks by means of node removal. Apparently, both star-shaped and ring-shaped graphs are fragile to intentional attacks.
4 is an example of a nontrivial graph G with four nodes N(G) = {A, B, C, D} and four edges E(G) = {AB, AC, BC, CD}, in which AB denotes an edge joining node A and node B, and so on. Every well-defined portion of a graph is a subgraph of that graph. 4, the triangle ABC is a subgraph of the whole graph, and so are the node D, the edge AB, the piecewise line BCD, etc. 6 A few examples of different types of graphs: (a) an undirected and unweighted simple graph with same type of nodes; (b) an undirected and unweighted graph with different types of nodes and edges; (c) an undirected but weighted graph with weights on both nodes and edges closed connection like the triangle ABC is called a circuit (or cycle) in the graph.
Since every node has degree larger than or equal to two, such a node vi+1 exists. Since the graph has finitely many nodes, the walk eventually connects to a node that has been chosen before. This walk yields a circuit in the graph. 8 A simple connected graph is Eulerian if and only if the degree of every node of the graph is an even number. 22 (b) (c) Examples of graphs: (a) Eulerian; (b) semi-Eulerian; (c) non-Eulerian graphs Fundamentals of Complex Networks 36 Proof. Suppose that the connected graph G is Eulerian, containing a trail T.