We introduce the notion of the degree of incidence of a vertex and an edge in a fuzzy graph in fuzzy graph theory. We concentrate on incidence, where the edge is adjacent to the vertex. We determine results concerning bridges, cutvertices, cutpairs, fuzzy incidence paths, fuzzy incidence tree for fuzzy incidence graphs. In (Dinesh, Ph.D. thesis, Kannur University, Kerala, India, ; Dinesh, Adv Fuzzy Sets Syst, 21:33–48, 2016, ), Dinesh introduced the notion of the degree of incidence of a vertex and an edge in fuzzy graph theory. This notion seem to have potential use in a variety of areas involving networks, Mordeson (Adv Fuzzy Sets Syst, 22:121–133, 2016, ).