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Dots and Lines - Anthony Bonato ***

Networks are of huge significance to life and technology, so it was refreshing to read a popular maths title on the subject. I was a little concerned when, in the introductory chapter, Anthony Bonato spent quite a while discussing network/graph theory jargon - we really don't need to know that a network is referred to as G with nodes represented by V and edges by E, let alone the meaning of 'heavy tailed'. There is absolutely no need to have such technical-speak in a popular title.  Unfortunately, he goes bombarding us with terminology in further chapters: it can be painful, especially when we are told a directed graph is known as a digraph, when I suspect most people outside of the graph theory community would consider a digraph a two letter phoneme.

Despite the relentless terminology we do learn a lot about networks and their applications, from Google's PageRank to Bacon numbers and from COVID infections to optimising security camera placement. As a writer, I was interested in the examination of character networks in books, though I would have liked to have seen a justification for linking characters if (and only if) their names appeared '15 words or less apart' in the text - it seems an arbitrary decision which should be justified.

The writing style was sometimes a touch saccharin. For example, on the night of the 2016 US election we are told that Bonato and a colleague 'stopped by a campus café, where I savoured a peppermint tea and a vegan cookie, reclining in a comfy chair.' Apart from confirming stereotypes about academics, this kind of thing really adds very little to the narrative that's of interest to the reader.

This is a difficult book to rate, neither fish nor fowl - it's a bit too technical for the general reader, but vague in its description of models and algorithms for someone with a mathematical or computing background. So, for example, we are told that the Louvain algorithm is one of the best for finding communities in networks. Apparently it uses the 'technical notion of modularity', but a detailed discussion of modularity is 'beyond our scope here', so we just get a vague sentence on what it does. In terms of discovering the range of potential applications of networks/graph theory, it's solidly four star, but I can't give it that as a satisfying popular maths title.

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