Download A first course in network theory by Ernesto Estrada, Philip A. Knight PDF

By Ernesto Estrada, Philip A. Knight

The research of community thought is a hugely interdisciplinary box, which has emerged as a massive subject of curiosity in numerous disciplines starting from physics and arithmetic, to biology and sociology. This publication promotes the varied nature of the learn of advanced networks by way of balancing the desires of scholars from very varied backgrounds. It references the main favourite options in community idea, provides Read more...

summary: The research of community conception is a hugely interdisciplinary box, which has emerged as a big subject of curiosity in a variety of disciplines starting from physics and arithmetic, to biology and sociology. This booklet promotes the various nature of the examine of advanced networks via balancing the desires of scholars from very assorted backgrounds. It references the main prevalent thoughts in community thought, presents examples in their functions in fixing sensible difficulties, and transparent symptoms on tips on how to examine their effects. within the first a part of the publication, scholars and researchers will become aware of the quantitative and analytical instruments essential to paintings with advanced networks, together with the main simple suggestions in community and graph concept, linear and matrix algebra, in addition to the actual suggestions most often used for learning networks. they are going to additionally locate guide on a few key abilities similar to the right way to facts analytic effects and the way to control empirical community info. the majority of the textual content is targeted on teaching readers at the most respected instruments for contemporary practitioners of community idea. those comprise measure distributions, random networks, community fragments, centrality measures, clusters and groups, communicability, and native and worldwide homes of networks. the combo of conception, instance and process which are offered during this textual content, should still prepared the scholar to behavior their very own research of networks with self assurance and make allowance lecturers to choose applicable examples and difficulties to coach this topic within the lecture room

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Extra resources for A first course in network theory

Example text

In Gl , n = 4 and m = 4. Since m > (n – 1)(n – 2)/2 we know it must be connected without any additional information. Network connectivity Consider a network representing social relationships. One would expect certain parts of the network to be more connected than others. That is, one would expect groups of mutual acquaintances to be linked together by more tenuous connections. This is definitely a matter that is worth analysing, so let us formalize some ideas about connectedness. We can compare networks by having a measure of connectivity.

Weighted networks are very useful if we want to assign a hierarchy to edges in a network, but in this book their appearances are very rare. 1) are ⎡ 0 ⎢1 ⎢ ⎢ ⎣1 0 1 0 1 0 1 1 0 1 ⎤ ⎡ 0 1 ⎢1 0⎥ ⎥ ⎢ ⎥ and ⎢ 1⎦ ⎣1 0 0 1 0 3 0 1 3 0 1 ⎤ 0 0⎥ ⎥ ⎥. 1⎦ 0 (ii) If G is a simple network with adjacency matrix A then its complement, G, has adjacency matrix E – I – A, where E is a matrix of ones. (iii) Starting with the cycle graph Cn we can add edges so that each node is linked to its k nearest neighbours clockwise and anticlockwise.

Then there exists at least one pair of adjacent nodes that lie in the same partition Vi . Label these node vp and vq . 5. Suppose that the distance between v1 and vp is k and that between v1 and vq is l. Now construct a closed walk that moves from v1 to vp along a shortest path; then from vp to vq along their common edge; and finally back from vq to v1 along a shortest path. This walk is closed and has length k + l + 1, which must be odd. Make connections between concepts 37 6. Because every closed walk of odd length contains an odd cycle we conclude that the network has an odd cycle, which contradicts our initial assumption and so the network must be bipartite.

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