Social capital and social support are two key constructs in the study of social networks and health. Despite their importance, little research has sought to examine the characteristics of those social ties by which individuals access social capital and support resources. Network diversity - a key structural feature in accessing social capital - refers to a person's broad but generally weak and heterogeneous social ties; core network size - a key structural feature in accessing social support - refers to the close, strong ties in personal networks. Our study examines whether the tie strength composing network diversity and core network size varies according to age-, psychosocial-, or health-related characteristics. Data came from the Montreal Neighbourhood Networks and Healthy Aging (MoNNET-HA) study, a representative sample of 2707 Montreal, Canada adults. Position and name generators were used to collect data on network diversity and core networks, and whether access to social resources was through kin, friends, or acquaintances. Multilevel negative binomial regression was used to account for the counts of different tie strengths nested within individuals and tracts. Network diversity and core network size both declined with older age groups, with those declines being more noticeable in not having ties at all or fewer ties with friends. Psychosocial and health factors altered the relative contribution of kin, friends and acquaintances to network diversity and core network size in similar patterns. Understanding the tie composition of network diversity and core network size can contribute to our knowledge of the social mechanisms linking social capital and support to health outcomes.