By Ernesto Estrada, Philip A. Knight

ISBN-10: 0198726457

ISBN-13: 9780198726456

The examine of community thought is a hugely interdisciplinary box, which has emerged as a huge subject of curiosity in a variety of disciplines starting from physics and arithmetic, to biology and sociology. This booklet promotes the varied nature of the learn of advanced networks by means of balancing the wishes of scholars from very diverse backgrounds. It references the main regularly occurring innovations in community thought, providesRead more...

summary: The research of community thought is a hugely interdisciplinary box, which has emerged as an immense subject of curiosity in quite a few disciplines starting from physics and arithmetic, to biology and sociology. This publication promotes the various nature of the examine of advanced networks through balancing the wishes of scholars from very various backgrounds. It references the main wide-spread suggestions in community concept, presents examples in their purposes in fixing useful difficulties, and transparent symptoms on find out how to examine their effects. within the first a part of the ebook, scholars and researchers will observe the quantitative and analytical instruments essential to paintings with complicated networks, together with the main easy techniques in community and graph conception, linear and matrix algebra, in addition to the actual suggestions most often used for learning networks. they are going to additionally locate guideline on a few key talents equivalent to find out how to facts analytic effects and the way to govern empirical community facts. the majority of the textual content is concentrated on teaching readers at the most dear instruments for contemporary practitioners of community idea. those comprise measure distributions, random networks, community fragments, centrality measures, clusters and groups, communicability, and native and international houses of networks. the mix of concept, instance and procedure which are awarded during this textual content, should still prepared the scholar to behavior their very own research of networks with self belief and make allowance lecturers to pick acceptable examples and difficulties to educate this topic within the school room

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**Additional info for A first course in network theory**

**Sample text**

Then the square matrix A = (aij ) is called the adjacency matrix of G. The adjacency matrix gives an unambiguous representation of any simple network. In much of the rest of this book we will look at how concepts in matrix algebra can be applied to networks and interpreting the results. Directed networks and networks with loops have adjacency matrices, too. One or two of our examples so far have had duplicate edges. We can represent this in our adjacency matrix by letting the appropriate entries in the adjacency matrix equal the number of connections between nodes.

N}. 3 Suppose G = (V , E) is a simple network where V = {1, 2, . . , n}. For 1 ≤ i, j ≤ n define aij = 1, 0, (i, j) ∈ E, (i, j) ∈ / E. Then the square matrix A = (aij ) is called the adjacency matrix of G. The adjacency matrix gives an unambiguous representation of any simple network. In much of the rest of this book we will look at how concepts in matrix algebra can be applied to networks and interpreting the results. Directed networks and networks with loops have adjacency matrices, too. One or two of our examples so far have had duplicate edges.

All of this information is readily gleaned from the diagrammatic form of the network, but the adjacency matrix encodes all this information in a way that can be manipulated algebraically. Notice that every entry of the diagonal of A2 is nonzero. None of these entries represents a circuit: they are ‘out and back again’ walks along edges. Since the diagonal of A3 is zero, there are no triangles in the network: the only circuits are permutations of 2 → 3 → 7 → 6 → 2. 4 Network connectivity A network is connected if there is a path connecting any two nodes.