The Cosmic Web is a complex network of filaments, walls and voids that represent the largest structures in the Universe. In this network, which is the direct result of structure formation, galaxy clusters occupy central positions as the nodes, connected through the filaments. In this work, we investigate the position in the Cosmic Web of one of the most known and best studied clusters of galaxies, the Coma cluster. We make use of the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) Main Galaxy Sample and of the Discrete Persistent Structure Extractor (DisPerSE ) to detect large scale filaments around the Coma cluster and we analyse the properties of the Cosmic Web. We study the network of filaments around Coma in a 75 Mpc radius region. We find that the Coma cluster has a median connectivity of 2.5, in agreement with measurements from clusters of similar mass in the literature, as well as with what expected from numerical simulations. It is indeed connected to 3 secure filaments which connect Coma to Abell 1367 and to several other clusters in the field. The location of these filaments in the vicinity of Coma is consistent with features detected in the X-ray, as well as the likely direction of infall of galaxies, as for example NGC4839. The overall picture that emerges of the Coma cluster is that of a highly connected structure occupying a central position as a dense node of the Cosmic Web. We also find a tentative detection, at 2.1σ significance, of the filaments in the SZ signal.